{"id":40,"date":"2023-09-17T11:00:07","date_gmt":"2023-09-17T11:00:07","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d1%86%d0%b5%d0%bf%d0%be%d1%87%d0%ba%d0%b0-%d0%bf%d1%80%d0%b0%d0%b2%d0%b8%d0%bb\/"},"modified":"2023-09-17T11:00:07","modified_gmt":"2023-09-17T11:00:07","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d1%86%d0%b5%d0%bf%d0%be%d1%87%d0%ba%d0%b0-%d0%bf%d1%80%d0%b0%d0%b2%d0%b8%d0%bb","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d1%86%d0%b5%d0%bf%d0%be%d1%87%d0%ba%d0%b0-%d0%bf%d1%80%d0%b0%d0%b2%d0%b8%d0%bb\/","title":{"rendered":"\u0426\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e (\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435)"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0438 \u043a\u0430\u043a \u0432\u044b\u0432\u043e\u0434\u0438\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445, \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430, \u0438 \u0434\u0430\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445 \u043f\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-regla-de-la-cadena\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0426\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u2014 \u044d\u0442\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0430\u044f \u0434\u043b\u044f \u0432\u044b\u0432\u043e\u0434\u0430 \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439.<\/strong> \u0426\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0433\u043b\u0430\u0441\u0438\u0442, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <em>f(g(x))<\/em> \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 <em>f'(g(x))<\/em> \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e <em>g'(x)<\/em> . <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/regle-de-la-chaine.webp\" alt=\"\u041f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u0438\" class=\"wp-image-2207\" width=\"269\" height=\"269\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f <\/span><\/p>\n<p> \u041d\u0435\u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u0447\u0430\u0441\u0442\u043e \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e\u0431\u044b <em>\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438 \u0437\u0430\u0442\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0438\u0442\u044c \u0435\u0435 \u043d\u0430 \u0442\u043e, \u0447\u0442\u043e \u0432 \u043d\u0435\u0439 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f<\/em> .<\/p>\n<p> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u043c \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u043b\u0435\u0433\u0447\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e, \u0435\u0441\u043b\u0438 \u0431\u044b \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0431\u044b\u043b\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0435\u0434\u0435\u043b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u043d\u0430\u043c \u043f\u0440\u0438\u0448\u043b\u043e\u0441\u044c \u0431\u044b \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u043c\u043d\u043e\u0433\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439.<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0430 \u043d\u0435 \u043a\u0430\u043a\u0438\u0445-\u043b\u0438\u0431\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438\u043b\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0441 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043e\u0447\u0435\u043d\u044c \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u043e\u0439 \u043e\u0448\u0438\u0431\u043a\u043e\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u0432 \u0442\u0430\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430\u0445, \u043a\u0430\u043a \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-de22604d9af306981b71d39bd190df75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x)\\cdot x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"68\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u274c<\/p>\n<p> \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e <strong>\u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043e\u0434\u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u043d\u0443\u0442\u0440\u0438 \u0434\u0440\u0443\u0433\u043e\u0439<\/strong> .<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea93fb0bbc6f1ac5c2e26f2c5730627f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"45\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u2705 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-con-la-regla-de-la-cadena\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u043e\u0432 \u0441 \u0446\u0435\u043f\u043d\u044b\u043c \u043f\u0440\u0430\u0432\u0438\u043b\u043e\u043c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430, \u043c\u044b \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430. \u041f\u043e\u043c\u043d\u0438\u0442\u0435, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u0432 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0432\u044b \u043d\u0435 \u043f\u043e\u043d\u0438\u043c\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0432\u044b\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0446\u0435\u043f\u043e\u0447\u043a\u0438, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0437\u0430\u0434\u0430\u0442\u044c \u043d\u0430\u043c \u0432\u043e\u043f\u0440\u043e\u0441 \u0432 \u043a\u043e\u043c\u043c\u0435\u043d\u0442\u0430\u0440\u0438\u044f\u0445!<\/p>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u0440 1<\/h3>\n<p> \u0412 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-056e8e809ecf361f98a9ab4a6509e1a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u0440\u0430\u0432\u043d\u0430 1 \u0440\u0430\u0437\u0443 \u0435\u0433\u043e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4537be7e40864f78dd4bf5a5cdfb53ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'\\bigl(g(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -7px;\"><\/p>\n<p> \u0431\u044b\u0442\u044c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82f88b45158f1890a0e60b2496a1898e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"331\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b66cdf74d9a89d4259495d799042e18c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\ln(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\cfrac{1}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"396\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f x, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u0430\u044f \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0434\u0432\u043e\u0439\u043a\u0438, \u0440\u0430\u0432\u043d\u0430 2x:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0f0a7b2d096f09aacc349fe800f5ae6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u044f \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e. \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u0434\u0432\u0443\u0445 \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0445 \u043d\u0430\u043c\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ad6b9a4a227664b616ffeef61781e54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x^2}\\cdot 2x = \\cfrac{2x}{x^2}=\\cfrac{2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"458\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u0440 2<\/h3>\n<p> \u0412\u043e \u0432\u0442\u043e\u0440\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043c\u044b \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1fd64daeb147f4af91e5eb8518621081_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^2+4x-5\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"179\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u043e\u043c\u0435\u0441\u0442\u0438\u0442\u044c \u043f\u0435\u0440\u0435\u0434 \u043d\u0435\u0439 \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0439 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0438 \u0432\u044b\u0447\u0435\u0441\u0442\u044c \u0438\u0437 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f \u043e\u0434\u043d\u0443 \u0435\u0434\u0438\u043d\u0438\u0446\u0443, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0435\u0437 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u0431\u044b\u043b\u0430 \u0431\u044b:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d0e7fc8a11cbd2103465a57128a9db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\left(3x^2+4x-5\\right)^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=3\\left(3x^2+4x-5\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"582\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0432\u043e\u0434\u0438\u043c \u0442\u043e, \u0447\u0442\u043e \u0432 \u0441\u043a\u043e\u0431\u043a\u0430\u0445:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dad3522b805cdb0c38e771bc6e630f50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=3x^2+4x-5\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=6x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"424\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u0434\u0432\u0443\u0445 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u044b\u0445 \u0440\u0430\u043d\u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d4d80ad509263a9791efd441621d183_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^2+4x-5\\right)^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=3\\left(3x^2+4x-5\\right)^2\\cdot (6x+4)\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"582\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u0440 3<\/h3>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u043d\u0430\u0439\u0434\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430 x \u0432 \u043a\u0443\u0431\u0435 \u043f\u043b\u044e\u0441 7x:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42b994d7e38385bd61050cc50428beeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3+7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e, \u044d\u0442\u043e \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f x <sup>3<\/sup> +7x \u0432\u043d\u0443\u0442\u0440\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0438\u043d\u0443\u0441\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u0421 \u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u2013 \u044d\u0442\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0432\u043d\u0435\u0448\u043d\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0443\u0434\u0435\u0442 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0441 \u0442\u0435\u043c \u0436\u0435 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u043e\u043c, \u0447\u0442\u043e \u0438 \u0441\u0438\u043d\u0443\u0441:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4b784343e9e483f8f3e2bb0cd465335_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}(x^3+7x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\text{cos}(x^3+7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"522\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0410 \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0445 <sup>3<\/sup> +7\u0445 \u0440\u0430\u0432\u043d\u0430 3\u0445 <sup>2<\/sup> +7.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-395ee5862baf231657c05660e22bbd42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^3+7x\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=3x^2+7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"392\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u0434\u0432\u0443\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5b44098b23fd39005532d5f42593f585_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3+7x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^3+7x)\\cdot (3x^2+7)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"555\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-con-la-regla-de-la-cadena\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u0412\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b84ea805fb8c56d493151d0f9b72b628_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(5x^2-6x\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"149\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412\u043d\u0435\u0448\u043d\u044f\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82e232ad4bd7b0f1b4b93625bd8dcf2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=a\\bigl(g(x)\\bigr)^n \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=n\\cdot a\\bigl(g(x)\\bigr)^{n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"397\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-058311927ac43c45c1de7d799d802310_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\left(5x^2-6x\\right)^3\\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= 3\\left(5x^2-6x\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"415\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0437\u0430\u0442\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u043d\u0443\u0442\u0440\u0438. \u042d\u0442\u043e \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0435\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043a \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u0438\u0437 \u0435\u0435 \u0447\u043b\u0435\u043d\u043e\u0432 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eda0577ba91756ce6852219b0b1bf4c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=ax^n \\ \\longrightarrow \\ f'(x)=n\\cdot ax^{n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4b1fc6c2a94bb4e9833be8140196f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=5x^2-6x\\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1c9d99adf81a8861bbd2dee3b8a7fcee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g'(x)=2\\cdot 5x^1-1 \\cdot 6 x^0 =10x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u043e\u0440\u043e\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3e6ffbcb906ced150b00cf463b56434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(5x^2-6x\\right)^3 \\ \\longrightarrow \\ \\bm{f'(x)= 3\\left(5x^2-6x\\right)^2\\cdot (10x-6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u0420\u0435\u0448\u0438\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c6ecb2411e5245a58c614748280b4568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-3\\left(5x^5+9x^3\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"182\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0432\u043d\u0435\u0448\u043d\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e5d21c7196c7ebaeaf6ca11762ca251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr) &amp; =4 \\cdot ( -3) \\left(5x^5+9x^3\\right)^3 \\\\[1.5ex]&amp;=-12\\left(5x^5+9x^3\\right)^3 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"357\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0430\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0432\u043d\u0443\u0442\u0440\u0435\u043d\u043d\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe839a2f2eb9412f63700dab70bf18f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=5x^5+9x^3\\ \\longrightarrow \\ g'(x)=25x^4+27x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"335\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0fe8c7e374a30ed8bcf0a83cea68d6bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-3\\left(5x^5+9x^3\\right)^4 \\ \\longrightarrow \\ \\bm{f'(x)=-12\\left(5x^5+9x^3\\right)^3\\cdot \\left(25x^4+27x^2\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"549\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-555bcc9c8b61b47c73e2014749954305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{2x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"87\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u042d\u0442\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f52dc9e8ea936ea4de492bb3be18ebb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{x} \\ \\longrightarrow \\ f'(x)=e^{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"204\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02e55bcf16e8288e1729ed5a4d06ed9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=e^{2x^3} \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= e^{2x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"281\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0436\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043e\u0442 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b17b1c7b9b871d8404166d92d5cb0974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=2x^3 \\ \\longrightarrow \\ g'(x)=6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0446\u0435\u043b\u043e\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0439 \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad4635f85ae781dd1565a8f6581d26c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{2x^3} \\ \\longrightarrow \\ \\bm{f'(x)= e^{2x^3}\\cdot 6x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0441\u043b\u043e\u0436\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a10feee3fd85abefa9ec5ea79c0cf223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{\\text{sen}(x) +x }\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u042d\u0442\u043e \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0432 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0435 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e. \u0418\u0442\u0430\u043a, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043e\u0442 \u043a\u043e\u0440\u043d\u044f: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64a603462f094d4c699c56453463ca49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x} \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"265\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e909efbe50930f94cce0b2485b060046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\sqrt[3]{\\text{sen}(x) +x } \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= \\cfrac{1}{3\\sqrt[3]{\\bigl(\\text{sen}(x) +x\\bigr)^2 }}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"455\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u0442\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u043e\u0442 \u0440\u0430\u0434\u0438\u043a\u0430\u043b\u0430. \u042d\u0442\u043e \u0441\u0443\u043c\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0431\u0443\u0434\u0435\u0442 \u0441\u0443\u043c\u043c\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0447\u043b\u0435\u043d\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffa1d177a8dfe81684225dffd555e6fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=\\text{sen}(x) +x \\ \\longrightarrow \\ g'(x)=\\cos(x) + 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"326\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044e \u0434\u0432\u0443\u0445 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fad132b49a5faab86a3955efd5422973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f(x)=\\sqrt[3]{\\text{sen}(x)+x} \\ \\longrightarrow \\ f'(x)&amp; = \\cfrac{1}{3\\sqrt[3]{\\bigl(\\text{sen}(x) +x\\bigr)^2 }} \\cdot \\bigl(\\cos(x) + 1 \\bigr)\\\\[1.5ex]&amp;=\\cfrac{\\bm{\\cos(x) + 1}}{\\bm{3\\sqrt[3]{\\bigl(\\mathbf{sen}(x) +x\\bigr)^2} }}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"509\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 5<\/h3>\n<p> \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438, \u0432\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09f37b7970003fc0221e15dccc157ccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x^2+5}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"100\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u0432\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0438 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430, \u0430 \u0437\u0430\u0442\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0438\u0442\u044c \u0438\u0445. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432\u044b\u0432\u043e\u0434\u0438\u043c \u043c\u043e\u0449\u043d\u043e\u0441\u0442\u044c \u043f\u043e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9fb428e4d74e0f972130fde4e48ac0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a^x \\ \\longrightarrow \\ f'(x)=a^x\\cdot \\ln (a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"256\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1d18c3443d6398dcefba063ac556cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=3^{x^2+5} \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= 3^{x^2+5}\\cdot  \\ln(3)\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"355\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u043e-\u0432\u0442\u043e\u0440\u044b\u0445, \u043c\u044b \u0432\u044b\u0432\u043e\u0434\u0438\u043c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438\u0437 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6070c83f8944ee39ae4e3e6e125bcc72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2+5 \\ \\longrightarrow \\ g'(x)=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"235\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u0442 \u043d\u0430\u043c, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0445 \u043d\u0430\u043c\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bc0c78749a089e832984e3844345b6f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x^2+5} \\ \\longrightarrow \\ \\bm{f'(x)= 3^{x^2+5}\\cdot  \\ln(3) \\cdot 2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"337\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 6 <\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c85e9125bf4f54041c798dc4cc8975d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln \\bigl(4x^2 \\cdot \\cos(x) \\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"174\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435 \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u0430\u044f, \u0442\u0430\u043a \u043a\u0430\u043a \u0432 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0435 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0440\u0430\u0437\u043d\u044b\u0445 \u0432\u0438\u0434\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0418\u0442\u0430\u043a, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a18d7f43ff1861389379485ae00db981_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x) \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"223\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b6ac8614a0671889738a762d0be9c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\ln \\bigl(4x^2 \\cdot \\cos(x) \\bigr) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= \\cfrac{1}{4x^2 \\cdot \\cos(x) }\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"430\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u043e-\u0432\u0442\u043e\u0440\u044b\u0445, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438\u0437 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430. \u042d\u0442\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0432\u044b\u0432\u043e\u0434\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd35f94998c8450bd2e65e92eeecea2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x) \\cdot g(x) \\ \\longrightarrow \\ z'(x)=f'(x)\\cdot g(x)+f(x) \\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"439\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-643ddf7ec82cbcc3bc685ceadf59da98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}g(x)=4x^2 \\cdot \\cos(x) \\ \\longrightarrow \\ g'(x) &amp; = 8x\\cdot \\cos(x) + 4x^2 \\cdot \\bigl(- \\text{sen}(x)\\bigr) \\\\[2ex] &amp; = 8x\\cdot \\cos(x) - 4x^2 \\cdot  \\text{sen}(x)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"472\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0446\u0435\u043b\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0441\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0443 \u0446\u0435\u043f\u043e\u0447\u043a\u0438, \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u0434\u0432\u0443\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6912d0951fb85a61df21cbed282000f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;= \\cfrac{1}{4x^2 \\cdot \\cos(x) } \\cdot \\bigl( 8x\\cdot \\cos(x) - 4x^2 \\cdot  \\text{sen}(x) \\bigr)\\\\[1.5ex]&amp;=\\cfrac{8x\\cdot \\cos(x) - 4x^2 \\cdot\\text{sen}(x)}{4x^2 \\cdot \\cos(x)}\\\\[1.5ex]&amp;=\\cfrac{\\bm{2\\cos(x) - x \\cdot }\\mathbf{sen}\\bm{(x)}}{\\bm{x \\cdot \\cos(x) }}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"169\" width=\"368\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 7<\/h3>\n<p> \u0420\u0435\u0448\u0438\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3eb7a0c588b3aac39a2a4aa49a691598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_9 (e^{x^2}-6x^7)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u042d\u0442\u043e \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c \u0438 \u0435\u0433\u043e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e, \u0430 \u0437\u0430\u0442\u0435\u043c \u043f\u0435\u0440\u0435\u043c\u043d\u043e\u0436\u0430\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435.<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c \u043f\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044e 9: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c3339cb70e45253b4994a0c740202cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a (x) \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{x\\cdot \\ln (a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"289\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0b4fc286244d6e5e35b8f7e94961314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\log_9 (e^{x^2}-6x^7) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=\\cfrac{1}{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"479\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430. \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u0447\u0438\u0441\u043b\u043e e \u0438\u043c\u0435\u0435\u0442 \u0432 \u0441\u0432\u043e\u0435\u043c \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0442. \u0435. \u044d\u0442\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u0442\u0430\u043a\u0436\u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34065617ade6fb28fe66bc3f57a49cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h(x)=e^{x^2} \\ \\longrightarrow \\ h'(x)=e^{x^2}\\cdot \\bigl(x^2\\bigr)' =e^{x^2}\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"348\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0446\u0435\u043b\u043e\u0433\u043e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f7cd729a06f3cde16890b587693a667_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)= e^{x^2}-6x^7\\ \\longrightarrow \\ g'(x)=e^{x^2}\\cdot 2x - 42x^6\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"352\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c f'(g(x)) \u0438 g'(x): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a702df902c9f1eff66e14836a262c0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{1}{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)} \\cdot \\bigl(e^{x^2}\\cdot 2x - 42x^6\\bigr)\\\\[1.5ex]&amp;=\\cfrac{\\bm{e^{x^2}\\cdot 2x - 42x^6}}{\\bm{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"342\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 8<\/h3>\n<p> \u0412\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0fa2f9b67e41d5edc5bbef249f598359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"231\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u043c \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044f \u0438\u0437 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u043f\u0440\u0438\u0434\u0435\u0442\u0441\u044f \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437. \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0432\u0435\u0434\u0435\u043c \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0438\u0437 \u0441\u0438\u043d\u0443\u0441\u0430, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0440\u0430\u0432\u043d\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b6d04ed6e1b20f210641bb48c25c2c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=\\cos\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"569\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430 \u0441\u0438\u043d\u0443\u0441\u0430, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e1c2492990456e277e493c898cb3924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} g(x)= \\Bigl( 9x^5 + \\cos(x) \\Bigr)^2 \\cdot g'(x) &amp;= 2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(9x^5 + \\cos(x) \\Bigr)' \\\\[1.5ex]&amp;=2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(45x^4-\\text{sen}(x)\\Bigr)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"519\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0441\u043d\u043e\u0432\u0430 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0432\u0441\u0435\u0433\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db5ac3368ea7d37f280e0f538aaed1a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f'(x)=\\cos } \\bm{\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr) \\cdot 2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(45x^4-}\\mathbf{sen}\\bm{(x)\\Bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"510\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-regla-de-la-cadena\"><\/span> \u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u0434\u043e\u043a\u0430\u0436\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0430\u0447\u043d\u0435\u043c \u0441 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc1699622d128f888c1f20599aeccf60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"219\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u041f\u0443\u0441\u0442\u044c <em>z<\/em> \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0430\u044f \u0438\u0437 \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a650ba7c58d41f371d90a56e4d4fd4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=f\\bigl(g(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"90\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0422\u043e\u0433\u0434\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <em>z<\/em> \u0441 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0431\u0443\u0434\u0435\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9419bc1d5617600c2ffea842822efed7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"269\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u0432\u044b \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u0442\u0435, \u0434\u0440\u043e\u0431\u044c \u043c\u043e\u0436\u043d\u043e \u0443\u043c\u043d\u043e\u0436\u0430\u0442\u044c \u0438 \u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0430 \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435, \u0432\u0435\u0434\u044c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043e\u0442 \u044d\u0442\u043e\u0433\u043e \u043d\u0435 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0448\u0430\u0433\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18ff4ca3bcd8ba04a25aa0187b3b5b3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{h}\\cdot \\frac{g(x+h)-g(x)}{g(x+h)-g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u041f\u0435\u0440\u0435\u0441\u0442\u0430\u0432\u0438\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0438 \u0434\u0440\u043e\u0431\u0435\u0439:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9059bbff916941c2e161b6d127ec654e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{g(x+h)-g(x)}\\cdot \\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u0438\u043c\u0435\u043d\u044f\u044f \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u0432\u044b\u0448\u0435\u0443\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0434\u0432\u0430. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0440\u0430\u0432\u0435\u043d \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044e \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-220a40fee3825089394f3d6e5578c4eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{g(x+h)-g(x)}\\cdot \\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"436\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0418 \u044d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8188c6fac1c61928975e7a8c02ac79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"175\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043c\u044b \u043f\u0440\u0438\u0448\u043b\u0438 \u043a \u043d\u0435\u0439 \u0438\u0437 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0446\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0438 \u043a\u0430\u043a \u0432\u044b\u0432\u043e\u0434\u0438\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445, \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430, \u0438 \u0434\u0430\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445 \u043f\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u043e\u0447\u043a\u0438? \u0426\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u2014 \u044d\u0442\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0430\u044f \u0434\u043b\u044f \u0432\u044b\u0432\u043e\u0434\u0430 \u0441\u043b\u043e\u0436\u043d\u044b\u0445 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d1%86%d0%b5%d0%bf%d0%be%d1%87%d0%ba%d0%b0-%d0%bf%d1%80%d0%b0%d0%b2%d0%b8%d0%bb\/\"> <span class=\"screen-reader-text\">\u0426\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e (\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435)<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 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