{"id":32,"date":"2023-09-17T11:03:23","date_gmt":"2023-09-17T11:03:23","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%be%d0%b5-%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/"},"modified":"2023-09-17T11:03:23","modified_gmt":"2023-09-17T11:03:23","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%be%d0%b5-%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0","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%be%d0%b5-%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/","title":{"rendered":"\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0438\u0437 \u0433\u0440\u0443\u0434\u0438"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430 (\u0444\u043e\u0440\u043c\u0443\u043b\u0443). \u0412\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430, \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0434\u0430\u0436\u0435 \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-seno\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0438\u043d\u0443\u0441\u0430 \u2013 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 x \u0440\u0430\u0432\u043d\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0443 x.<\/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-2fdc142e7ff766dcf7fcd24b16e11ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"375\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0415\u0441\u043b\u0438 \u0432 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0435 \u0441\u0438\u043d\u0443\u0441\u0430 \u043f\u0440\u0438\u0441\u0443\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \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 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u044b\u0439 \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \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-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u042d\u0442\u0430 \u0432\u0442\u043e\u0440\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0434\u043b\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435\u043c \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u043a \u043f\u0435\u0440\u0432\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435. \u0418\u0442\u0430\u043a, \u0432\u043a\u0440\u0430\u0442\u0446\u0435, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u0430 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-du-sinus.webp\" alt=\"\u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0439 \u0438\u0437 \u0433\u0440\u0443\u0434\u0438\" class=\"wp-image-1872\" width=\"392\" height=\"282\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-seno\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0443\u0432\u0438\u0434\u0435\u043b\u0438, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u0430, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u043f\u043e\u043d\u044f\u043b\u0438, \u043a\u0430\u043a \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0441\u0438\u043d\u0443\u0441\u0430. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-seno-de-2x\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 1: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8eb4985d571a4ead05f1f6289197249f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0435 \u0441\u0438\u043d\u0443\u0441\u0430 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u0442\u043b\u0438\u0447\u043d\u0430\u044f \u043e\u0442 x, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0441\u0438\u043d\u0443\u0441\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-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f 2x \u0440\u0430\u0432\u043d\u0430 2, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 2x \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 2x \u043d\u0430 2. <\/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-c3fdd6b2afbc2c387f9160474119139f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(2x)\\cdot 2=2\\text{cos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"503\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-seno-de-x-al-cuadrado\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 2: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 x \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-856ab4d35ee160a6b966a748ec9cf4f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\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-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0410 \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0445 <sup>2<\/sup> \u0440\u0430\u0432\u043d\u0430 2\u0445, \u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u0445, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0433\u043e \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c 2, \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-901d9c0780a330a0d10d9f6d0185bbe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"423\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-seno-al-cubo\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 3: \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u0432 \u043a\u0443\u0431\u0435<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6428f8178ef3b768b1ec0a673f31c814_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}^3(x^5+4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"162\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0434\u0440\u0443\u0433\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \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 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0434\u043b\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0441\u0438\u043d\u0443\u0441\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-18d979f3aa2169f80fd46a26a7c70bf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"402\" 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 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ec8461861a7213d371d7dc6cff1cc92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3\\text{sen}^2(x^5+4x)\\cdot \\text{cos}(x^5+4x)\\cdot (5x^4+4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"368\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <u style=\"text-decoration-color:#ff951b;\">\u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u044d\u0442\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c<\/u> <span style=\"text-decoration: underline;\"> \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 <\/span> .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"segunda-derivada-del-seno\"><\/span>\u0412\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0417\u0430\u0442\u0435\u043c \u043c\u044b \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0438\u043d\u0443\u0441\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443, \u0431\u0443\u0434\u0443\u0447\u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043e\u043d\u0430 \u0438\u043c\u0435\u0435\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438.<\/p>\n<p> \u041a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432\u044b\u0448\u0435, \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. \u0418\u0442\u0430\u043a, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0440\u0430\u0432\u043d\u0430 \u0441\u0438\u043d\u0443\u0441\u0443, \u043d\u043e \u043f\u043e\u043c\u0435\u043d\u044f\u043b\u0430 \u0437\u043d\u0430\u043a. \u042d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e <strong>\u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u2014 \u044d\u0442\u043e \u0441\u0430\u043c \u0441\u0438\u043d\u0443\u0441, \u043d\u043e \u0441 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u043d\u044b\u043c \u0437\u043d\u0430\u043a\u043e\u043c<\/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-7a312c69d71be2df495ba30f6e3b85e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{sen}(x)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=\\text{cos}(x)\\\\[2ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{sen}(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"157\" width=\"133\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041e\u0434\u043d\u0430\u043a\u043e \u0435\u0441\u043b\u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u0441\u0438\u043d\u0443\u0441\u0430 \u043d\u0435 \u0440\u0430\u0432\u0435\u043d x, \u044d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u0441\u044f, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u0435\u0440\u0435\u0442\u0430\u0449\u0438\u0442\u044c \u0442\u0435\u0440\u043c\u0438\u043d \u0446\u0435\u043f\u043d\u043e\u0433\u043e \u043f\u0440\u0430\u0432\u0438\u043b\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-a6a3a1255d5494e320a50ef02bce9d19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{sen}(u)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=\\text{cos}(u)\\cdot u' \\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{sen}(u)\\cdot u'^2 +\\text{cos}(u)\\cdot u'' \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"153\" width=\"263\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-del-seno-inverso\"><\/span>\u041e\u0431\u0440\u0430\u0442\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u0430\u043a \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e, \u043a\u0430\u0436\u0434\u0430\u044f \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u0441\u0438\u043d\u0443\u0441 \u0442\u0430\u043a\u0436\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c.<\/p>\n<p> <strong>\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430<\/strong> \u0440\u0430\u0432\u043d\u0430 \u0447\u0430\u0441\u0442\u043d\u043e\u043c\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\u0430, \u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043a\u043e\u0440\u0435\u043d\u044c \u0438\u0437 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u043c\u0438\u043d\u0443\u0441 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442\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-8fbeb5e099f046c572b9076a3e65b80b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}^{-1}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"412\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u043c\u043d\u0438\u0442\u0435, \u0447\u0442\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u0441\u0438\u043d\u0443\u0441 \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0430\u0440\u043a\u0441\u0438\u043d\u0443\u0441\u043e\u043c.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043e\u0431\u0440\u0430\u0442\u043d\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 \u043e\u0442 5x \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-6946743939fbacc11ac050625151ea97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}^{-1}(5x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{5}{\\sqrt{1-(5x)^2}}=\\cfrac{5}{\\sqrt{1-25x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"553\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-seno\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91a8a2e764daa0e57ffd835005c8c474_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sen}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" 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-e80e9e86c1ff2373d4321dbf0b348d8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{sen}(x^2+5x-9)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"210\" 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-acda934e5f1e150c3657c7c179dae04e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }\\displaystyle f(x)=\\text{sen}\\left(\\frac{x}{4}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"144\" 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-b5dd5bfe722128418bd89665bb3d7fc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sen}^4(5x^3-10x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"214\" 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-25cef83962dcc595ea141212c144424c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sen}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"161\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1761cfbdc805de80c6edab26613014cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f(x)=2\\text{sen}(x^4-3x^3)-7\\text{sen}^2(x^5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0c6093fe6364e806ee4adb980e6ae1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=7\\text{cos}(7x)\" 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-0c4f15d01ad3f2dae29e0e6e4944b050_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\text{cos}(x^2+5x-9)\\cdot (2x+5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"290\" 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-5ec1bb477b6f8b9d62adffa38288667b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }\\displaystyle f'(x)=\\text{cos}\\left(\\frac{x}{4}\\right)\\cdot \\frac{1}{4}=\\frac{\\text{cos}\\left(\\frac{x}{4}\\right)}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"256\" 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-4d54d16bf947c61429cb47f9613701cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=4\\text{sen}^3(5x^3-10x^2)\\cdot \\text{cos}(5x^3-10x^2)\\cdot (15x^2-20x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"473\" 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-9a5b66e0c4e67d903aea56caef9e72df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f'(x)=\\text{cos}\\bigl(\\ln(x)\\bigr)\\cdot \\cfrac{1}{x} =\\cfrac{\\text{cos}\\bigl(\\ln(x)\\bigr)}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"296\" 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-d5002d567a4412d1a78c369ff26ebb66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f'(x)=2\\text{cos}(x^4-3x^3)\\cdot (4x^3-9x^2)-14\\text{sen}(x^5)\\cdot \\text{cos}(x^5)\\cdot 5x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"504\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-del-seno\"><\/span> \u0414\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435 \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 x \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u043e\u043c x, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u0430 \u0438\u043c\u0435\u043d\u043d\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-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> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u044b\u0432\u043e\u0434\u0438\u043c\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u2014 \u044d\u0442\u043e sin(x), \u043f\u043e\u044d\u0442\u043e\u043c\u0443:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9af97a03363cd676667ad58135760ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{sen}(x+h)-\\text{sen}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"247\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u0421\u0438\u043d\u0443\u0441 \u0441\u0443\u043c\u043c\u044b \u043c\u043e\u0436\u043d\u043e \u043f\u0435\u0440\u0435\u043f\u0438\u0441\u0430\u0442\u044c, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043e:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0836929c5c4ae666d530ad9946e1a191_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}(a+b)=\\text{sen}(a)\\text{cos}(b)+\\text{cos}(a)\\text{sen}(b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"308\" 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-dbebd45e9fdfaa9e6ade3b6a4bfad716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{sen}(x)\\text{cos}(h)+\\text{cos}(x)\\text{sen}(h)-\\text{sen}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"381\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0434\u0440\u043e\u0431\u044c \u0432 \u0434\u0432\u0435 \u0434\u0440\u043e\u0431\u0438 \u0441 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435\u043c. \u041c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u043e\u0434\u0435\u043b\u0430\u0442\u044c \u044d\u0442\u0443 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044e \u0431\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f \u0437\u0430\u043a\u043e\u043d\u0443 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0441\u0443\u043c\u043c\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-3368ab9ecc3a19ad382f85707d6e66cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\left[\\frac{\\text{sen}(x)(\\text{cos}(h)-1)}{h}+\\frac{\\text{cos}(x)\\text{sen}(h)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"375\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-819a10da8fb503b9797c855f0a6208bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\text{sen}(x)\\frac{\\text{cos}(h)-1}{h}+\\lim_{h \\to 0}\\text{cos}(x)\\frac{\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"377\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0437\u0430\u043a\u043e\u043d\u044b \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432. <\/span><\/p>\n<p> \u0427\u043b\u0435\u043d\u044b \u0441\u0438\u043d\u0443\u0441 x \u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 x \u043d\u0435 \u0437\u0430\u0432\u0438\u0441\u044f\u0442 \u043e\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f h, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0438\u0445 \u0437\u0430 \u043f\u0440\u0435\u0434\u0435\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-2ae7a3b5022abcb1941be4a0b6a02287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{sen}(x)\\cdot\\lim_{h \\to 0}\\frac{\\text{cos}(h)-1}{h}+\\text{cos}(x)\\cdot\\lim_{h \\to 0}\\frac{\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"402\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u0412\u0441\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0441\u0435\u0439\u0447\u0430\u0441, \u044d\u0442\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u044d\u0442\u0438 \u0434\u0432\u0430 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\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-14300dcf4010d732b8568b9b4460b5e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{\\text{sen}(x)}{x}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"116\" 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-51835176b411ca1ec4f37835a83685fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 0}\\frac{1-\\text{cos}(x)}{x}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"146\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u041f\u0440\u0438\u043c\u0435\u0447\u0430\u043d\u0438\u0435.<\/strong> \u0414\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0430\u0446\u0438\u044e \u0434\u0432\u0443\u0445 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0445 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u0438\u0441\u043a\u0430\u0442\u044c \u0432 \u043f\u043e\u0438\u0441\u043a\u043e\u0432\u0438\u043a\u0435 \u043d\u0430\u0448\u0435\u0433\u043e \u0441\u0430\u0439\u0442\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-cfbe7d4af77ff230e9e7a059414e90e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{sen}(x)\\cdot 0+\\text{cos}(x)\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"223\" 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-863dc523f1b112a07352b60c8dfdc2b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"109\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0418 \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u043c\u044b \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u043c, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 x \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u043e\u043c x.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430 (\u0444\u043e\u0440\u043c\u0443\u043b\u0443). \u0412\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430, \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0434\u0430\u0436\u0435 \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u0430. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430? \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0438\u043d\u0443\u0441\u0430 \u2013 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u0430 x \u0440\u0430\u0432\u043d\u0430 &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%be%d0%b5-%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/\"> <span class=\"screen-reader-text\">\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043e \u0438\u0437 \u0433\u0440\u0443\u0434\u0438<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[6],"tags":[],"class_list":["post-32","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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