{"id":31,"date":"2023-09-17T11:03:43","date_gmt":"2023-09-17T11:03:43","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-%d0%bf%d0%be%d1%82%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8-%d0%bc\/"},"modified":"2023-09-17T11:03:43","modified_gmt":"2023-09-17T11:03:43","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%bf%d0%be%d1%82%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8-%d0%bc","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-%d0%bf%d0%be%d1%82%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8-%d0%bc\/","title":{"rendered":"\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 (\u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438)"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u043a\u0430\u043a \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044c (\u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e), \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0434\u0430\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044f \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-potencia\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043d\u0430 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0435 \u0432 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435 \u043c\u0438\u043d\u0443\u0441 1 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0435 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f.<\/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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0441\u043b\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <span style=\"text-decoration: underline;\"> \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f <\/span> , \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u043f\u0440\u043e\u0441\u0442\u043e \u0443\u043c\u043d\u043e\u0436\u044c\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043d\u0430 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0438 \u0432\u044b\u0447\u0442\u0438\u0442\u0435 \u0438\u0437 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043e\u0434\u043d\u0443 \u0435\u0434\u0438\u043d\u0438\u0446\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-46eb5b8a4c6968ca5e37af417fd2fb31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430 1.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0435\u0441\u0442\u044c \u0434\u0432\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b: \u043f\u0435\u0440\u0432\u0443\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0441\u0435\u0433\u0434\u0430, \u0438 \u0432\u0442\u043e\u0440\u0443\u044e, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435, \u0435\u0441\u043b\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f x. <\/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\/derivee-dune-puissance.webp\" alt=\"\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0435 \u043e\u0442 \u0441\u0438\u043b\u044b\" class=\"wp-image-1760\" width=\"354\" height=\"264\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u041c\u044b \u043c\u043e\u0436\u0435\u043c \u043b\u0435\u0433\u043a\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u043f\u0435\u0440\u0432\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u0430\u044f \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u0430 \u0432\u0442\u043e\u0440\u043e\u0439, \u043d\u043e \u0441 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0446\u0435\u043f\u043e\u0447\u043a\u0438.<\/p>\n<p> \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u044d\u0442\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435, \u0435\u0441\u043b\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u0438. \u0415\u0441\u043b\u0438 x \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435, \u0432\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-potencias\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0441\u0442\u0435\u043f\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0443\u0432\u0438\u0434\u0435\u043b\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \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\u043e\u0439 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043f\u043e\u043d\u044f\u043b\u0438, \u043a\u0430\u043a \u0432\u044b\u0432\u043e\u0434\u044f\u0442\u0441\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-potencia-de-base-x\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 1: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0431\u0430\u0437\u043e\u0432\u043e\u0439 \u043c\u043e\u0449\u043d\u043e\u0441\u0442\u0438 x<span class=\"ez-toc-section-end\"><\/span><\/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-1a77d84e8f9a9d165a989ae8edd67a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043b\u0438 \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435, \u043a\u043e\u0433\u0434\u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e x, \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\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-46eb5b8a4c6968ca5e37af417fd2fb31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 x, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c 4, \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-b4f99a41ebf24ffb9dc9d375925fbb03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=4\\cdot x^{4-1}=4x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-potencia-con-parentesis\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 2: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0441 \u043a\u0440\u0443\u0433\u043b\u044b\u043c\u0438 \u0441\u043a\u043e\u0431\u043a\u0430\u043c\u0438<span class=\"ez-toc-section-end\"><\/span><\/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-c7e7bcf1cc01f1609b200eb0707450f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(2x-1)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435 \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043e\u0431\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u0441\u043a\u043e\u0431\u043a\u0430\u0445 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0440\u0430\u0432\u043d\u0430 2. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432\u0441\u0435\u0439 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\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-8b3fb5d76dac22c3fad5ebe3a0cae630_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(2x-1)^5 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=5\\cdot (2x-1)^4\\cdot 2=10(2x-1)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"577\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-potencia-negativa\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 3: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438<span class=\"ez-toc-section-end\"><\/span><\/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-0bb49a61d47e399ec84ffddce840b4a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(\\log 9x)^{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439, \u0430 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \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 \u0434\u043b\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u0430\u0436\u0435 \u0435\u0441\u043b\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439, \u0438\u0437 \u043d\u0435\u0433\u043e \u0442\u043e\u0436\u0435 \u043d\u0443\u0436\u043d\u043e \u0432\u044b\u0447\u0435\u0441\u0442\u044c. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \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-b883e28fe86b43bae53225fbfc0989c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-2\\cdot (\\log 9x)^{-3}\\cdot \\cfrac{1}{9x\\cdot \\ln 10}\\cdot 9 =\\cfrac{-2(\\log 9x)^{-3}}{x\\ln 10}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"412\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0415\u0441\u043b\u0438 \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c \u043a\u0430\u043a\u0438\u0435-\u043b\u0438\u0431\u043e \u0441\u043e\u043c\u043d\u0435\u043d\u0438\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043e\u0437\u043d\u0430\u043a\u043e\u043c\u0438\u0442\u044c\u0441\u044f \u0441 \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0437\u0434\u0435\u0441\u044c:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-4-derivada-de-una-potencia-con-raiz\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 4: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0441 \u043a\u043e\u0440\u043d\u0435\u043c<span class=\"ez-toc-section-end\"><\/span><\/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-74c457eaa374d11591afb05c08c79a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{(5x+2)^7}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"149\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0432 \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u043d\u043e\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0438. \u041e\u0434\u043d\u0430\u043a\u043e \u0440\u0430\u0434\u0438\u043a\u0430\u043b\u044b \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u044c \u0432 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043c\u043e\u0436\u043d\u043e \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c, \u043f\u0440\u0435\u0432\u0440\u0430\u0442\u0438\u0432 \u0435\u0435 \u0432 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0441 \u0434\u0440\u043e\u0431\u043d\u044b\u043c \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0435\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-a851a10c275664fd40272c3f18ebb696_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(5x+2)^{\\frac{7}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0418 \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-48032a3f39b346214870d2930c0e070f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{7}{3}\\cdot (5x+2)^{\\frac{7}{3}-1} \\cdot 5=\\cfrac{35}{3}(5x+2)^{\\frac{4}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"314\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u0442\u044c \u044d\u0442\u0438 \u0442\u0438\u043f\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043a\u043e\u0440\u043d\u0435\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0435 \u043e\u0442 \u043a\u043e\u0440\u043d\u044f <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-una-potencia\"><\/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\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412\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\u0438\u0445 \u0441\u0442\u0435\u043f\u0435\u043d\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-8439a4f480db3b28403219b3d6c617c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"101\" 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-586b1cce6da03d26fc251a34f15b8713_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=3x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"110\" 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-2048513ae93bb32ac7333db56114f8f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=-2x^{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" 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-61b9db052aa145257ef92ac543621b69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=(3x^2-4x)^6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" 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-234c4c2a85b56e062d186e33461534c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=6(x^2+10)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"170\" 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-888598e68e596f15e1e4b585c2287c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\cfrac{1}{(9x+2)^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"156\" 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-bc2353357a484e175ac77e99e4446cb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G) } f(x)=\\sqrt{4x^5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" 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-3e21d4a7733a95b407d4a53114146489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H) } \\displaystyle f(x)=\\left(x^2-4x+\\frac{1}{3}\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"210\" 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-c04e44f3e248cec297f4476885e22a25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I) } f(x)=\\text{sen}^3(6-2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"172\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32e3eaeb51430921053c75da627cacd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=8x^7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"115\" 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-44e8de4cfb9cb267005e390e06c393e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=15x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" 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-4394259c55b711c8668f4d72e3bd4766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=8x^{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"125\" 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-8a916b5238f094595e63d04a86303a7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=6(3x^2-4x)^5\\cdot (3x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" 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-698c94329d2e6edc002bf2b99d4de74e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=3\\cdot 6(x^2+10)^2 \\cdot 2x=36x(x^2+10)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"358\" 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-b2c94d0e23facd72c3a85241bfc4552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=-3\\cdot (9x+2)^{-4}\\cdot 9 =-27(9x+2)^{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"363\" 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-9f488aced09f0e560280f5ce55a1b002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G) } f'(x)=\\cfrac{5}{2}\\cdot 2x^{\\frac{5}{2}-1} =5x^{\\frac{3}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"211\" 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-19d1d31c8415cb654940148ec1a25835_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H) } \\displaystyle f'(x)=4\\left(x^2-4x+\\cfrac{1}{3}\\right)^3\\cdot (2x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"303\" style=\"vertical-align: -23px;\"><\/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-aa9c91854971313e88fde0d535c5a6c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I) } f'(x)=3\\text{sen}^2(6-2x)\\cdot \\text{cos}(6-2x)\\cdot (-2)=-6x\\cdot \\text{sen}^2(6-2x)\\cdot \\text{cos}(6-2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"599\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u043a\u0430\u043a \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044c (\u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e), \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0434\u0430\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044f \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043d\u0430 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0435 \u0432 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435 \u043c\u0438\u043d\u0443\u0441 1 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0435 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0441\u043b\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c &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-%d0%bf%d0%be%d1%82%d0%b5%d0%bd%d1%86%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8-%d0%bc\/\"> <span class=\"screen-reader-text\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 (\u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438)<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[6],"tags":[],"class_list":["post-31","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438 (\u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f)<\/title>\n<meta name=\"description\" content=\"\u041c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c (\u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e). \u2705 \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 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