{"id":36,"date":"2023-09-17T11:02:01","date_gmt":"2023-09-17T11:02:01","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%81%d1%83%d0%bc%d0%bc%d1%8b\/"},"modified":"2023-09-17T11:02:01","modified_gmt":"2023-09-17T11:02:01","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d1%81%d1%83%d0%bc%d0%bc%d1%8b","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%81%d1%83%d0%bc%d0%bc%d1%8b\/","title":{"rendered":"\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0438\u0437 \u0441\u0443\u043c\u043c\u044b"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u0443\u043c\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 (\u0444\u043e\u0440\u043c\u0443\u043b\u0443). \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 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441\u0443\u043c\u043c \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 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0443\u043c\u043c\u044b. \u0418 \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u0430\u0441 \u0436\u0434\u0435\u0442 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-suma\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u044b \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0440\u0430\u0432\u043d\u0430 \u0441\u0443\u043c\u043c\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043a\u0430\u0436\u0434\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438.<\/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-cec257ea65c3d37da6460f8f1ab6bb1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)+g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)+g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"463\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043f\u043e \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438, \u0430 \u0437\u0430\u0442\u0435\u043c \u0438\u0445 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0430 \u0437\u0430\u0442\u0435\u043c \u0432\u0437\u044f\u0442\u0438\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439. <\/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-somme.webp\" alt=\"\u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0438\u0437 \u0441\u0443\u043c\u043c\u044b\" class=\"wp-image-2035\" width=\"243\" height=\"243\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c\u043e \u043a \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438 \u043f\u0435\u0440\u0435\u0434 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0441\u0442\u043e\u0438\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0437\u043d\u0430\u043a \u0432\u043c\u0435\u0441\u0442\u043e \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e, \u043c\u044b \u0442\u0430\u043a\u0436\u0435 \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u0443 \u0436\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u0435\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\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-6a93098fe108be6019d44ba2d0f82108_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)\\pm g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\pm g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"463\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u2014 \u044d\u0442\u043e \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f, \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0449\u0430\u044f \u0430\u0441\u0441\u043e\u0446\u0438\u0430\u0442\u0438\u0432\u043d\u044b\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e\u043c, \u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0449\u0438\u043c, \u0447\u0442\u043e \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0439, \u0443\u0447\u0430\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0445 \u0432 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0438, \u0431\u0435\u0437\u0440\u0430\u0437\u043b\u0438\u0447\u043d\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \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\u0434\u043e\u043b\u0436\u0430\u0442\u044c \u043e\u0441\u0442\u0430\u0432\u0430\u0442\u044c\u0441\u044f \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u0430\u0436\u0434\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-05ceda7dfbdbac4960b012f62d17c8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=f(x)\\pm g(x) \\pm h(x)\\pm \\dots\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex]z'(x)=f'(x)\\pm g'(x)\\pm h'(x)\\pm \\dots\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-una-suma\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b<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, \u043a\u0430\u043a\u043e\u0432\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b, \u043c\u044b \u0443\u0432\u0438\u0434\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\u044b\u0445 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u043f\u043e\u043d\u044f\u0442\u044c, \u043a\u0430\u043a \u0432\u044b\u0432\u043e\u0434\u044f\u0442\u0441\u044f \u0441\u0443\u043c\u043c\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-suma-de-funciones-potenciales\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 1: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u044b \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<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-efca27bad0818b86e6e42ee15a31ed6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3x^2+5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"125\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u044b \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u0430\u0436\u0434\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \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 \u043a\u0430\u0436\u0434\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-69\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e625836da38ce78d816c887fd842fff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ 3x^2=6x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"95\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f575779fe1f9c29e907e67f622cb5411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 5x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\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 \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0443\u0434\u0435\u0442 \u0441\u0443\u043c\u043c\u043e\u0439 \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-8a8dcfca37df757df3fd79292ead67b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=6x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-suma-de-funciones-diferentes\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 2: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u044b \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<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-0c94ae34a2f2fe6741b9233bde69c420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x)+\\ln(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"166\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u0443\u043c\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0434\u0432\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e, \u0430 \u0437\u0430\u0442\u0435\u043c \u0441\u043b\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 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-72\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e1fd0d9e783b091d26fe14a6f9523801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ \\text{sen}(x)=\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"144\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-630f2b7757bfc7fbc7fe540313c526b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\ln (x)=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"103\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> \u0410 \u0437\u0430\u0442\u0435\u043c \u0434\u043e\u0431\u0430\u0432\u043b\u044f\u0435\u043c \u0434\u0432\u0435 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\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-d74c893fd6ae38b019a934d75b39b921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{cos}(x)+\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"145\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-suma-al-cuadrado\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 3: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u044b \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435<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-fc55182666ca330acaf33748f94e1b06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^4+7x^2+1\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u0438\u043c\u0435\u0435\u043c \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0442\u0430\u043a \u043a\u0430\u043a \u0438\u043c\u0435\u0435\u043c \u0441\u0443\u043c\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u0443\u044e \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\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 \u0432\u0441\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-3d5f04a22b460b05368b60eba4a74c4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2\\left(3x^4+7x^2+1\\right)\\cdot (12x^3+14x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"303\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-de-sumas-de-funciones\"><\/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\u0443\u043c\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0439<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0441\u0443\u043c\u043c\u044b \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-ae19a6909252c6385e64b78c67688db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=6x^3+9x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"159\" 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-d7239b728b0ae9ef7f14e34910f71c8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=x^4+10x^3+5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" 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-d421d72da5a4af38dda14af4151fba4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=3x^2-4x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" 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-2df5e88a0c25ffd19b52aa2c950a1c1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{cos}(x)+e^{3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"177\" 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-3f844607b5234ee8282802ef2ad19dac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\left(x^3+4x^2+6x\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"213\" 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-202ed150e3c26b6b56de412d7f8a5884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\log_3(8x^2+2x)-x^7+e^{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"277\" 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-c5e6d4e0f405a797739dba71003c60ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=18x^2+18x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"174\" 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-1069a5e43f43a569cfb3db5f8d9b7331_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=4x^3+30x^2+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-93b4f2f1938846ce64f102e4964cbbef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=6x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" 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-190b6cc92e8c9a9119d0255247b7e14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=-\\text{sen}(x)+3e^{3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"205\" 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-fa0eabdbceafaf3e9b7535da9d1d520a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=3\\left(x^3+4x^2+6x\\right)^2\\cdot (3x^2+8x+6)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"354\" 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-40fc02db80aa8a889f70ca9f25d295c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{16x+2}{(8x^2+2x)\\ln(3)}-7x^6+2x\\cdot e^{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"334\" 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-formula-de-la-derivada-de-una-suma\"><\/span> \u0414\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u044d\u0442\u043e\u043c \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435 \u043c\u044b \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0418 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u043f\u0440\u0438\u0431\u0435\u0433\u0430\u0435\u043c \u043a \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\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-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> \u0422\u043e\u0433\u0434\u0430 \u043f\u0443\u0441\u0442\u044c z \u0431\u0443\u0434\u0435\u0442 \u0441\u0443\u043c\u043c\u043e\u0439 \u0434\u0432\u0443\u0445 \u0440\u0430\u0437\u043d\u044b\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-4d2d91569fa3b33d834dead8ca02ff3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)+g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" 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-17f0dc216847872551637f676d1ff0b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{z(x+h)-z(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"215\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c z \u0441\u0443\u043c\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0432 \u043f\u0440\u0435\u0434\u0435\u043b\u044c\u043d\u043e\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\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-feab6b99cc6e3bfad015b988f16c5241_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{\\bigl[f(x+h)+g(x+h)\\bigr]-\\bigl[f(x)+g(x)\\bigr]}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"389\" style=\"vertical-align: -13px;\"><\/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-73d3c0e1781a7ec65721ab6aef3d840a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)+g(x+h)-f(x)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"359\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u041c\u044b \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0434\u0440\u043e\u0431\u044c \u0432 \u0441\u0443\u043c\u043c\u0443 \u0434\u0432\u0443\u0445 \u0434\u0440\u043e\u0431\u0435\u0439, \u043a\u0430\u0436\u0434\u0430\u044f \u0438\u0437 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043a\u0430\u0436\u0434\u043e\u0439 \u0441\u0443\u043c\u043c\u0438\u0440\u0443\u044e\u0449\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-e7b00aae0064e00a5e8a2f57e54fa339_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\left[\\frac{f(x+h)-f(x)}{h}+\\frac{g(x+h)-g(x)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"379\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0411\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0434\u0432\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u0435\u0434\u0435\u043b \u0441\u0443\u043c\u043c\u044b \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d \u0441\u0443\u043c\u043c\u0435 \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-6c8091e8c717504ae86efff94b5d8e3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}+\\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"394\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u0418, \u043a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432\u044b\u0448\u0435 \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u043f\u0440\u0435\u0434\u0435\u043b\u0443 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\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-cea8c29e93381736297a8f6aa46c83fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f'(x)+g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u0443\u043c\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 (\u0444\u043e\u0440\u043c\u0443\u043b\u0443). \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 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441\u0443\u043c\u043c \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 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0443\u043c\u043c\u044b. \u0418 \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u0430\u0441 \u0436\u0434\u0435\u0442 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0443\u043c\u043c\u044b \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u044b \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0440\u0430\u0432\u043d\u0430 \u0441\u0443\u043c\u043c\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043a\u0430\u0436\u0434\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043f\u043e \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438, &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%81%d1%83%d0%bc%d0%bc%d1%8b\/\"> <span class=\"screen-reader-text\">\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0438\u0437 \u0441\u0443\u043c\u043c\u044b<\/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-36","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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