{"id":30,"date":"2023-09-17T11:04:26","date_gmt":"2023-09-17T11:04:26","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%ba%d0%be%d0%bd%d1%81%d1%82%d0%b0%d0%bd%d1%82%d1%8b\/"},"modified":"2023-09-17T11:04:26","modified_gmt":"2023-09-17T11:04:26","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%ba%d0%be%d0%bd%d1%81%d1%82%d0%b0%d0%bd%d1%82%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-%d0%ba%d0%be%d0%bd%d1%81%d1%82%d0%b0%d0%bd%d1%82%d1%8b\/","title":{"rendered":"\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0438\u0437 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u0442\u043e\u0438\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b (\u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438). \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0443\u0447\u0438\u043c \u0432\u0430\u0441 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0438 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u0432 \u0432\u0438\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f, \u0440\u0435\u0448\u0430\u044f \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"cual-es-la-derivada-de-una-constante\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u0432\u0441\u0435\u0433\u0434\u0430 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e<\/strong> , \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-2d766593916de27e212a34aef2054834_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"298\" 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 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u0442\u044c \u043d\u0438\u043a\u0430\u043a\u0438\u0445 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043f\u0440\u043e\u0441\u0442\u043e \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e.<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span style=\"text-decoration: underline;\"> \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <\/span> \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u043d\u0430\u043a\u043b\u043e\u043d\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-constantes\"><\/span> \u041f\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<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u043f\u043e\u043d\u044f\u0442\u044c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e:<\/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<p> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u0432\u0441\u0435\u0433\u0434\u0430 \u0434\u0430\u0435\u0442 0. \u041d\u0435\u0432\u0430\u0436\u043d\u043e, \u0431\u0443\u0434\u0435\u0442 \u043b\u0438 \u0437\u043d\u0430\u043a \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u0438\u043b\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c, \u0431\u0443\u0434\u0435\u0442 \u043b\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u043e\u0447\u0435\u043d\u044c \u0431\u043e\u043b\u044c\u0448\u0438\u043c \u0438\u043b\u0438 \u043e\u0447\u0435\u043d\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u043c, \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-de-una-constante\"><\/span> \u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432\u0435\u043b\u0438\u043a\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u043c\u044b \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c, \u043f\u043e\u0447\u0435\u043c\u0443 \u044d\u0442\u043e\u0442 \u0442\u0438\u043f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e.<\/p>\n<p> \u041f\u0443\u0441\u0442\u044c <em>f<\/em> \u2014 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0437\u043d\u0430\u0447\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-252f9958e223f77bf50cb3b92a7c3e35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \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 \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-1162892842eac60784851f1e85e8fdb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\lim_{h\\to 0}\\frac{f(a+h)-f(a)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"217\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 <\/span><\/p>\n<p> \u0418\u0442\u0430\u043a, \u0435\u0441\u043b\u0438 \u043c\u044b \u0440\u0435\u0448\u0438\u043c \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u043e\u0441\u0442\u043e\u044f\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-58d3f81dc74abeda947bde54da295ed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\lim_{h\\to 0}\\frac{f(a+h)-f(a)}{h}=\\frac{k-k}{h}=\\frac{0}{h}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"358\" style=\"vertical-align: -13px;\"><\/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 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430 0 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-constante-por-una-funcion\"><\/span> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u043f\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043e\u0434\u043d\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0442\u043e \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0435\u0437 \u043a\u0430\u043a\u0438\u0445-\u043b\u0438\u0431\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445. \u041d\u043e \u043a\u0430\u043a \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u044f\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0438\u0436\u0435 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442 \u0432 \u0441\u043e\u0447\u0435\u0442\u0430\u043d\u0438\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0432\u0438\u0434\u0430\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u0443\u044e \u043d\u0430 \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u0438\u043f \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u0430\u044f \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0440\u0430\u0432\u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0435, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\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-dc2d4fae6d8022adc2e0e59a11328e98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k\\cdot g(x)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"394\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\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-f2cfaac6bfb384965645704f65a77d73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2\\quad \\longrightarrow\\quad g'(x)=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u043d\u043d\u043e\u0439 \u043d\u0430 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0448\u0430\u0433\u0435, \u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2d78b626617c0c2b71c57c4c001806e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=5\\cdot x^2\\quad \\longrightarrow\\quad f'(x)=5\\cdot 2x=10x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"326\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-constante-entre-una-funcion\"><\/span> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u043c\u0435\u0436\u0434\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u043c\u0435\u0436\u0434\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044e \u043c\u043e\u0434\u0438\u0444\u0438\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u0443\u044e \u043d\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\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-a6f82edb233fb5397883601585b2c8b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{k}{g(x)}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{-k\\cdot g'(x)}{\\bigl[g(x)\\bigr]^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"398\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0434\u0435\u043b\u0435\u043d\u043d\u0430\u044f \u043d\u0430 \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \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-834aa396d04dc3dfbf9ed34179d01d21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{3}{8x}\\quad\\longrightarrow\\quad f'(x)=\\cfrac{-3\\cdot 8}{\\bigl[8x\\bigr]^2}=\\cfrac{-24}{64x^2}=\\cfrac{-3}{8x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"391\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f 8\u0445 \u0440\u0430\u0432\u043d\u0430 8. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-constante-elevada-a-una-funcion\"><\/span> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u044e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u0432 \u0432\u0438\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0440\u0430\u0432\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044e \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u0443\u044e \u0432 \u0432\u0438\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\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-ed673abdbd2d71c999fda55567b5caa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=k^{g(x)}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\ln(k)\\cdot k^{g(x)} \\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"452\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u2014 \u044d\u0442\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u0432 \u0441\u0438\u043d\u0443\u0441 \u0434\u0430\u0435\u0442: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d71aa1159f9dff572fa00b5e944c93e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2^{sen(x)}\\quad\\longrightarrow\\quad f'(x)=\\ln(2)\\cdot 2^{sen(x)} \\cdot cos(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-de-constantes\"><\/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 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0420\u0435\u0448\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1151947a5df3c80a9a82fd8dd7911d08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ f(x)=4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" 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-f3b9b9e60f638606f1ea9036d33ce6b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\ f(x)=99\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" 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-c5e39e91184c8e7a45c56c8426efb1d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ f(x)=-15\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ca70a6708b842b71580fbfbcecad546_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)}\\ f(x)=\\cfrac{3}{11}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"104\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ae5d06cf677fc7362db34b01de801a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)}\\ f(x)=\\sqrt{29}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"116\" 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-7807a5902d509572902cf9708bb432a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)}\\ f(x)=2\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-a4e7f6030a532ed32a9e433a44e75d19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G)}\\ f(x)=2\\cdot (3x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" 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-afe95ae68313d4e96b4116a4c1319dc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H)}\\ f(x)=\\cfrac{10}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"104\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d5568ffced02cb2bbb3d924529a8d5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I)}\\ f(x)=5^{x^3+2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"127\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0414\u043e \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f F) \u0432\u0441\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043f\u0440\u043e\u0441\u0442\u044b\u043c\u0438 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u044b\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0441\u0435 \u0438\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0434\u0430\u044e\u0442 \u043d\u043e\u043b\u044c. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1dd15b92eb6be305ddca9c2b0144e668_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" 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-5913671d5f624902abdc69992468520b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\ f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" 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-537e56da4a49f763a947286abf590ff2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" 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-d437a34237ec2e84285ff79023cf4650_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)}\\ f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" 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-1b14287ec6a36fa3e932c967addf81b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)}\\ f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" 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-4b6fa2b8bbd48622e1656c8e81f77f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)}\\ f'(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u0430\u0436\u0435 \u0435\u0441\u043b\u0438 \u044d\u0442\u043e \u0434\u0440\u043e\u0431\u044c \u0438\u043b\u0438 \u043a\u043e\u0440\u0435\u043d\u044c, \u0435\u0441\u043b\u0438 \u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0435\u0442 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u043e\u043d\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e.<\/p>\n<p class=\"has-text-align-left\"> \u041d\u0430\u043f\u0440\u043e\u0442\u0438\u0432, \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0442\u0440\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0441\u043e\u0431\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0441\u043e\u0431\u043e\u0439 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0438\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043d\u0430\u043c \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\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-deb38c5b02aa6a18a9f068256f5cafb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G)}\\ f'(x)=2\\cdot 3=6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" 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-56aa83b86415c5e5bf7156f896622879_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H)}\\ f'(x)=\\cfrac{-10\\cdot 2x}{\\bigl[x^2\\bigr]^2}=\\cfrac{-20x}{x^4}=\\cfrac{-20}{x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"303\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c909027a7982134fe162399678aeb794_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I)}\\ f(x)=\\ln(5)\\cdot 5^{x^3+2x}\\cdot (3x^2+2)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"260\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u0442\u043e\u0438\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b (\u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438). \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0443\u0447\u0438\u043c \u0432\u0430\u0441 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0438 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u0432 \u0432\u0438\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f, \u0440\u0435\u0448\u0430\u044f \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \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. \u041f\u043e\u044d\u0442\u043e\u043c\u0443, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\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-%d0%ba%d0%be%d0%bd%d1%81%d1%82%d0%b0%d0%bd%d1%82%d1%8b\/\"> <span class=\"screen-reader-text\">\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0438\u0437 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\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-30","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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