{"id":404,"date":"2023-07-03T00:18:18","date_gmt":"2023-07-03T00:18:18","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%b4%d0%b5%d1%80%d0%b8%d0%b2%d0%b0%d1%82%d0%b8%d0%b2%d1%8b\/"},"modified":"2023-07-03T00:18:18","modified_gmt":"2023-07-03T00:18:18","slug":"%d0%b4%d0%b5%d1%80%d0%b8%d0%b2%d0%b0%d1%82%d0%b8%d0%b2%d1%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%b4%d0%b5%d1%80%d0%b8%d0%b2%d0%b0%d1%82%d0%b8%d0%b2%d1%8b\/","title":{"rendered":"\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0442\u0438\u043f\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0412\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438 \u0438 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u043c\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u043f\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u043c. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formules-derivees.webp\" alt=\"\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b\" class=\"wp-image-2945\" width=\"226\" height=\"226\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-las-derivadas\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u044b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435<\/strong> \u2014 \u044d\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0435 \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, <strong>\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435<\/strong> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0438 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u044b\u0440\u0430\u0436\u0430\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u043a\u043e\u043c \u0448\u0442\u0440\u0438\u0445\u0430 <em>&#8216;<\/em> , \u0442\u043e \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f <em>f'(x)<\/em> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <em>f(x)<\/em> .<\/p>\n<p> \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u043c\u044b\u0441\u043b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 \u2014 \u044d\u0442\u043e \u043d\u0430\u043a\u043b\u043e\u043d \u043a\u0430\u0441\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-de-la-tangente-ligne.webp\" alt=\"\u0441\u043c\u044b\u0441\u043b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445\" class=\"wp-image-2306\" width=\"392\" height=\"391\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> <strong>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> \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 class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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> \u041e\u0434\u043d\u0430\u043a\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0431\u044b\u0447\u043d\u043e \u043d\u0435 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043e \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u0432\u044b\u0448\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0435, \u0430 \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u044e\u0442\u0441\u044f \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0442\u0438\u043f\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0412\u0441\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0432\u044b\u0432\u043e\u0434\u0430 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u044b \u043d\u0438\u0436\u0435.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-las-derivadas\"><\/span>\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0432\u0438\u0434\u0435\u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0434\u0435\u0440\u0438\u0432\u0430\u0442\u0438\u0432\u043e\u0432, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u043e\u043d\u0438 \u0441\u043e\u0437\u0434\u0430\u044e\u0442\u0441\u044f, \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0432 \u043a\u0430\u0436\u0434\u044b\u0439 \u0442\u0438\u043f \u0434\u0435\u0440\u0438\u0432\u0430\u0442\u0438\u0432\u043e\u0432 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435. \u0426\u0435\u043b\u044c \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0441\u0442\u0430 \u2014 \u043f\u043e\u043c\u043e\u0447\u044c \u0432\u0430\u043c \u0445\u043e\u0440\u043e\u0448\u043e \u043f\u043e\u043d\u044f\u0442\u044c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445, \u043f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438 \u0432 \u043a\u043e\u043d\u0446\u0435 \u043a\u043e\u043d\u0446\u043e\u0432 \u0443 \u0432\u0430\u0441 \u0432\u043e\u0437\u043d\u0438\u043a\u043d\u0443\u0442 \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 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0437\u0430\u0434\u0430\u0442\u044c \u0438\u0445 \u043d\u0430\u043c \u0432 \u043a\u043e\u043c\u043c\u0435\u043d\u0442\u0430\u0440\u0438\u044f\u0445.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-constante\"><\/span>\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0435 \u043e\u0442 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b<\/strong> \u0432\u0441\u0435\u0433\u0434\u0430 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e, \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\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-c7bd8f1aee171f251c313218820e22f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=k \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=0 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0435 \u043d\u0443\u0436\u043d\u043e \u0437\u0430\u043d\u0438\u043c\u0430\u0442\u044c\u0441\u044f \u043d\u0438\u043a\u0430\u043a\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u043e\u0439, \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e.<\/p>\n<p> \u0412\u0437\u0433\u043b\u044f\u043d\u0438\u0442\u0435 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-561a1b2c2b0347c0cb38ed7565e46fa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=3 \\qquad \\longrightarrow\\qquad f'(x)=0\\\\[3ex]g(x)=-5 \\qquad \\longrightarrow\\qquad g'(x)=0\\\\[3ex]h(x)=291 \\qquad \\longrightarrow\\qquad h'(x)=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"265\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-lineal\"><\/span> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> \u2014 \u044d\u0442\u043e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043f\u0440\u0438 \u0447\u043b\u0435\u043d\u0435 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <em>f(x)=Ax+B<\/em> \u0440\u0430\u0432\u043d\u0430 <em>A<\/em><\/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-c55a9a25283e37ab61dc79856ee92a11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=Ax+B\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=A \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412\u0437\u0433\u043b\u044f\u043d\u0438\u0442\u0435 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0431\u044b\u043b \u043f\u043e\u043b\u0443\u0447\u0435\u043d \u044d\u0442\u043e\u0442 \u0442\u0438\u043f \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-53d0d8c8814ef6884b442c3c50cce8a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=3x-1\\quad\\longrightarrow\\quad f'(x)=3\\\\[3ex]f(x)=5x\\quad\\longrightarrow\\quad f'(x)=5\\\\[3ex] f(x)=-2x+9\\quad\\longrightarrow\\quad f'(x)=-2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"280\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-potencia\"><\/span> \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0435 \u043e\u0442 \u0441\u0438\u043b\u044b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0438<\/strong> \u0438\u043b\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u2014 \u044d\u0442\u043e \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 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435, \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 \u043c\u0438\u043d\u0443\u0441 1.<\/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-1e7df9c631129b040e262f67f36b41be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \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 \u043e\u0434\u043d\u0443 \u0435\u0434\u0438\u043d\u0438\u0446\u0443.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043c\u043e\u0449\u043d\u043e\u0441\u0442\u0438 x \u0432 \u043a\u0443\u0431\u0435 \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-0c0dd56d2e4a99c896f5e035d51f80be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=3\\cdot x^{3-1}=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 (\u0438 \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0445) \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043c\u043e\u0436\u043d\u043e \u0437\u0434\u0435\u0441\u044c:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0440\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><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-raiz\"><\/span> \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0435 \u043e\u0442 \u043a\u043e\u0440\u043d\u044f<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><meta charset=\"utf-8\"> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0440\u043d\u044f,<\/strong> \u0438\u043b\u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\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 \u0438\u043d\u0434\u0435\u043a\u0441\u0430 \u043a\u043e\u0440\u043d\u044f, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0433\u043e \u043d\u0430 \u0442\u043e\u0442 \u0436\u0435 \u043a\u043e\u0440\u0435\u043d\u044c, \u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044e 1 \u0438\u0437 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f \u043f\u043e\u0434\u043a\u043e\u0440\u0435\u043d\u043d\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\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-8b8e85735674a043d4fb2c448038ceb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=1.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043a\u043e\u0440\u043d\u044f \u0438\u0437 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-5e879d493e8b67755617d2aed1743cde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{2\\sqrt{x^{2-1}}}=\\cfrac{1}{2\\sqrt{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"425\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0440\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 \u043a\u043e\u0440\u043d\u044f <\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-exponencial\"><\/span> \u041f\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 class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u041f\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<\/strong> \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0442\u043e\u0433\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0447\u0438\u0441\u043b\u043e <em>e<\/em> \u0438\u043b\u0438 \u0434\u0440\u0443\u0433\u043e\u0435 \u0447\u0438\u0441\u043b\u043e. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0434\u0432\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430, \u0438 \u0432\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u0443, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044e \u043c\u043e\u0449\u043d\u043e\u0441\u0442\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-c21e61c79c41a4f27d53a41495521bdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=a^x \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=a^x\\cdot \\ln(a)\\\\[3ex] f(x)=e^x \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=e^x \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0434\u0432\u0435 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-90bd19942de37daaf7af04179eaf5e91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=7^{x} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=7^x\\cdot \\ln(7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-71dd62c13ea22caa62fb0e8af338fbdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{x} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=e^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"312\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p><span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-logaritmica\"><\/span> \u041f\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 class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u041f\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<\/strong> \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443, \u0435\u0441\u043b\u0438 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u044b\u0439, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u0430 \u0435\u0441\u043b\u0438 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c \u0438\u043c\u0435\u0435\u0442 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u0434\u0440\u0443\u0433\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u0440\u0443\u0433\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-d384075ba6ad6dcfaf82949d33ad397b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=\\ln(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x}\\\\[3ex] f(x)=\\log_a(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(a)}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u043f\u043e \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044e 3 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-e61ac2c2f66f8b05dce8760bdec17d09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_3(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p><span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \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=\"derivadas-trigonometricas\"><\/span>\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0422\u0440\u0435\u043c\u044f \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u043c\u0438 <strong>\u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u043c\u0438<\/strong> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0438\u043d\u0443\u0441\u0430, \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430, \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0438\u043c\u0435\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0438\u0434:<\/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-a9e9d0157c2b1eb994571ba96aae4f26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=\\text{sen}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x)\\\\[2.5ex] f(x)=\\text{cos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(x)\\\\[1.1ex]f(x)=\\text{tan}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{\\text{cos}^2(x)}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0442\u0438\u043f\u043e\u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0442\u0430\u043a\u0438\u0445 \u043a\u0430\u043a \u0441\u0435\u043a\u0430\u043d\u0441, \u043a\u043e\u0441\u0435\u043a\u0430\u043d\u0441, \u043a\u043e\u0442\u0430\u043d\u0433\u0435\u043d\u0441, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u0442. \u0434. \u041d\u043e \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0447\u0430\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0434\u0440\u0438\u0444\u0442\u0430 \u2014 \u044d\u0442\u043e \u0442\u0440\u0438 \u0432\u044b\u0448\u0435\u043f\u0435\u0440\u0435\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u044b\u0445.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"reglas-de-derivacion\"><\/span> \u0440\u0435\u0444\u0435\u0440\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u043e\u0433\u0434\u0430 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0441 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u043f\u043e-\u0434\u0440\u0443\u0433\u043e\u043c\u0443. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f <strong>\u043f\u0440\u0430\u0432\u0438\u043b\u0430\u043c\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/strong> , \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f, \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\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-ba4f3225344df68c84b4437ecb0c7536_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}z(x)=f(x)\\pm g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\pm g'(x)\\\\[4ex] z(x)=f(x)\\cdot g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\cdot g(x)+f(x)\\cdot g'(x)\\\\[4ex]z(x)=\\cfrac{f(x)}{g(x)} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445, \u043d\u043e \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439.<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b \u0443\u0432\u0438\u0434\u0435\u043b\u0438, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430, \u043d\u0438\u0436\u0435 \u043c\u044b \u0440\u0435\u0448\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u044b:<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-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 class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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<p>\u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\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 \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u0447\u043b\u0435\u043d\u0443 \u0441\u0443\u043c\u043c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u043b\u0430\u0441\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438.<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0438\u0437 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430:<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-8c539c8db8dbf532a639e09af47a583a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=4^{x}\\cdot \\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0447\u043b\u0435\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0440\u0430\u0432\u043d\u0430 4 <sup>x<\/sup> ln(4), \u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u2014 \u043a\u043e\u0441\u0438\u043d\u0443\u0441. \u0418\u0442\u0430\u043a, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-5829940bb4219334d7e238b40a19794e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=4^{x}\\cdot \\ln (4) \\cdot \\text{sen}(x) +4^{x}\\cdot \\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u043d\u043e\u0433\u043e:<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-59b390fee61ab3c2cbb4dc2230386658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0412 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u0435 \u0438 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \u0434\u0440\u043e\u0431\u0438 \u0443 \u043d\u0430\u0441 \u0441\u0442\u043e\u0438\u0442 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043d\u0443\u0436\u043d\u043e \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u043d\u043e\u0433\u043e, \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f) \u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0438\u043c\u0435\u0435\u0442 \u0432\u043b\u0430\u0441\u0442\u044c: <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-af3f7cb513883d1fa5dadca23701c19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\\\[2ex]&amp;=\\cfrac{15x^4-24x^2+40x^3-64x-10x^4-40x^3}{25x^4+64-80x^2}\\\\[2ex]&amp;=\\cfrac{5x^4-24x^2-64x}{25x^4-80x^2+64}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"379\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-cadena\"><\/span> \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u0446\u0435\u043f\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><meta charset=\"utf-8\"> <strong>\u0426\u0435\u043f\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e<\/strong> \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. \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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-662d8c44c904e83267bbca5f968ca546_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1pt, boxsep=1.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      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) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u042d\u0442\u043e \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0434\u0435\u0440\u0438\u0432\u0430\u0442\u0438\u0432\u043e\u0432, \u043a\u0430\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u0441\u043b\u043e\u0436\u043d\u0435\u0435 \u0443\u0441\u0432\u043e\u0438\u0442\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043c\u044b \u043f\u043e\u044d\u0442\u0430\u043f\u043d\u043e \u0440\u0435\u0448\u0438\u043c \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\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-c1863b1f92befa398b5c8692d239abf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u043e \u0441\u0443\u0442\u0438, \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> \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 \u0434\u043e\u043b\u0436\u043d\u044b \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\u043e\u0441\u0442\u0430\u0432\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-2046d85a1440fe95dccc4d8bb553e2f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\text{cos}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"441\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u0410, \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0445 <sup>3<\/sup> \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \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-1d045f948b3519322ae6771bd4497d70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^3\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"320\" 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 \u0446\u0435\u043b\u043e\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0439 \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-ab755de02fa9196320c59676d77cd2e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^3)\\cdot 3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"430\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430. <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivabilidad-de-una-funcion\"><\/span> \u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> \u0432 \u0442\u043e\u0447\u043a\u0435 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<ul>\n<li> \u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u0442\u043e \u043e\u043d\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/li>\n<li> \u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0432 \u043a\u0430\u043a\u043e\u0439-\u0442\u043e \u0442\u043e\u0447\u043a\u0435, \u043e\u043d\u0430 \u0442\u0430\u043a\u0436\u0435 \u043d\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/li>\n<\/ul>\n<p> \u041e\u0434\u043d\u0430\u043a\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u0435 \u044d\u0442\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u043d\u0435\u0432\u0435\u0440\u043d\u043e, \u0442. \u0435. \u0442\u043e, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435, \u043d\u0435 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043e\u043d\u0430 \u0432\u0441\u0435\u0433\u0434\u0430 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/p>\n<p> \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0435\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430:<\/p>\n<ul>\n<li> \u0415\u0441\u043b\u0438 \u044d\u0442\u043e <strong>\u0433\u043b\u0430\u0434\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430,<\/strong> \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430.<\/li>\n<li> \u0415\u0441\u043b\u0438 \u044d\u0442\u043e <strong>\u0443\u0433\u043b\u043e\u0432\u0430\u044f \u0442\u043e\u0447\u043a\u0430,<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430, \u043d\u043e \u043d\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-3\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\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\/exercices-resolus-pour-representer-une-fonction-quadratique-incomplete.webp\" alt=\"\" class=\"wp-image-140\" width=\"250\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> <span style=\"color:#1976d2;\"><strong>\u0422\u043e\u0447\u043a\u0430 \u0441\u0433\u043b\u0430\u0436\u0438\u0432\u0430\u043d\u0438\u044f<\/strong><\/span> \u043f\u0440\u0438 x=0:<br \/> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\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\/comment-representer-graphiquement-une-fonction-avec-valeur-absolue.webp\" alt=\"\" class=\"wp-image-230\" width=\"286\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> <span style=\"color:#1976d2;\"><strong>\u041d\u0430\u043a\u043b\u043e\u043d\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430<\/strong><\/span> \u043f\u0440\u0438 x=2:<br \/> \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430, \u043d\u043e \u043d\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435.<\/p>\n<\/div>\n<\/div>\n<p> \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u043b\u0438 \u043a\u0443\u0441\u043e\u0447\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0432 <strong>\u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435<\/strong> \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435: <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 20px; border-radius:20px;\">\n<ul style=\"color:#64B5F6; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 \u043d\u0435 \u0440\u0430\u0432\u043d\u044b, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435:<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97c60c64dc01a7e0a9084313d15b0886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x_o^-) \\neq f'(x_o^+) \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u041e\u043d\u043e \u043d\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e \u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67ab403a6241009b92035b251f86c88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_o\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul style=\"color:#64B5F6; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442, \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430:<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f9477828318b9e6392465762f831642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x_o^-) = f'(x_o^+) \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0414\u0430, \u044d\u0442\u043e \u0432\u044b\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0432<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67ab403a6241009b92035b251f86c88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_o\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<\/div>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435 \u043a\u0443\u0441\u043e\u0447\u043d\u043e:<\/p>\n<ul>\n<li> \u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=2:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a98eee72521c68fd394eb6209a7d0a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=  \\left\\{ \\begin{array}{lcl} 3x^2-6x &amp; \\text{si} &amp;  x<2 \\\\[2ex] 6\\ln (x-1) &amp; \\text{si} &amp; x\\geq 2 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"249\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0431\u043e\u0438\u0445 \u0443\u0447\u0430\u0441\u0442\u043a\u043e\u0432 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b \u043d\u0430 \u0441\u0432\u043e\u0438\u0445 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430\u0445, \u043e\u0434\u043d\u0430\u043a\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 x=2. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0440\u0435\u0448\u0438\u043c \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\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-dad5bcb0055431aa87a67068c04d2ce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x\\to 2^-} f(x) = \\lim\\limits_{x\\to 2^-} \\bigl(3x^2-6x\\bigr) = 3\\cdot2^2-6\\cdot2=12-12=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"449\" style=\"vertical-align: -14px;\"><\/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-31e1ba2ea2c5fd9fa86e5cefed0e5535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x\\to 2^+} f(x) = \\lim\\limits_{x\\to 2^+} 6\\ln (x-1) = 6\\ln (2-1)=6 \\ln 1=6 \\cdot 0= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"474\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0432 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0434\u0430\u043b\u0438 \u043d\u0430\u043c \u0442\u043e\u0442 \u0436\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 x=2.<\/p>\n<p> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0443\u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 x = 2, \u043c\u044b \u0438\u0437\u0443\u0447\u0438\u043c \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c <strong>\u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435<\/strong> \u043a\u0443\u0441\u043e\u0447\u043d\u043e-\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\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-3709995609d0f69f382ff651e397c00a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)= \\left\\{ \\begin{array}{lcl} 6x-6 &amp; \\text{si} &amp;  x<2 \\\\[2ex] \\cfrac{6}{x-1} &amp; \\text{si} &amp; x\\geq 2 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043e\u0446\u0435\u043d\u0438\u043c \u043a\u0430\u0436\u0434\u0443\u044e \u0431\u043e\u043a\u043e\u0432\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0432 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\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-ca27189960575c1151402d040bfa76f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^-)=6\\cdot2-6=12-6 = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"239\" 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-058310a16d7d545ea56e99517845842b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^+)=\\cfrac{6}{2-1} = \\cfrac{6}{1} = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0414\u0432\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0434\u0430\u043b\u0438 \u043d\u0430\u043c \u043e\u0434\u0438\u043d \u0438 \u0442\u043e\u0442 \u0436\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u043f\u0440\u0438 x = 2, \u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0440\u0430\u0432\u043d\u043e 6:<\/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-aadf046f27916c46f0a302d6e0c34113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^-) = f'(2^+) = 6 \\ \\longrightarrow \\ \\bm{f'(2) = 6}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"275\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0435\u0441\u043b\u0438 \u0431\u044b \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0434\u0430\u043b\u0438 \u043d\u0430\u043c \u0434\u0440\u0443\u0433\u043e\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u043b\u043e \u0431\u044b, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u0430 \u043f\u0440\u0438 x=2. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0432 \u044d\u0442\u043e\u0442 \u043c\u043e\u043c\u0435\u043d\u0442 \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043b\u0430 \u0431\u044b.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u043d\u0430 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/span><\/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 \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0442\u0438\u043f\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0412\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438 \u0438 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u043c\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u043f\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u043c. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u044b? \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u2014 \u044d\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0435 \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0438 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u044b\u0440\u0430\u0436\u0430\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u043a\u043e\u043c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%b4%d0%b5%d1%80%d0%b8%d0%b2%d0%b0%d1%82%d0%b8%d0%b2%d1%8b\/\"> <span class=\"screen-reader-text\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435<\/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-404","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>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u2014 \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ru\/\u0434\u0435\u0440\u0438\u0432\u0430\u0442\u0438\u0432\u044b\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u2014 \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c\" \/>\n<meta property=\"og:description\" content=\"\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 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\u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u044b\u0435 \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0438 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u044b\u0440\u0430\u0436\u0430\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u043a\u043e\u043c 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