{"id":381,"date":"2023-07-03T20:49:06","date_gmt":"2023-07-03T20:49:06","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%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/"},"modified":"2023-07-03T20:49:06","modified_gmt":"2023-07-03T20:49:06","slug":"%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%be%d0%b4%d0%bd%d0%b0%d1%8f-%d0%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8","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%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/","title":{"rendered":"\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"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c, \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u0430 \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. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u0440\u0435\u0448\u0430\u0435\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439. \u0412\u044b \u0434\u0430\u0436\u0435 \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \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\u044b\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-de-una-funcion-lineal\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \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?<span class=\"ez-toc-section-end\"><\/span><\/h2>\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 \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<\/strong> , \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-da354d71cc8fcc91ec98275630d162d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=Ax+B\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=A\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"352\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0439 \u0447\u043b\u0435\u043d \u0443\u0434\u0430\u043b\u044f\u0435\u0442\u0441\u044f \u0438\u0437 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span style=\"text-decoration: underline;\"> \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b <\/span> \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e. \u0418, \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0447\u043b\u0435\u043d\u0430 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u043c \u044d\u0442\u043e\u0433\u043e \u0447\u043b\u0435\u043d\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\u0443\u043c\u043c\u044b \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u0432\u0438\u0434\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u043c \u043f\u0440\u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u043c \u0447\u043b\u0435\u043d\u0435. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-dune-fonction-lineaire.webp\" alt=\"\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\" class=\"wp-image-1739\" width=\"263\" height=\"224\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \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 \u2014 \u044d\u0442\u043e \u043d\u0430\u043a\u043b\u043e\u043d \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u0432\u044b\u0448\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u0443\u044e \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0441\u043e \u0441\u0432\u043e\u0435\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-funciones-lineales\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<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 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0447\u0442\u043e\u0431\u044b \u0437\u0430\u0432\u0435\u0440\u0448\u0438\u0442\u044c \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043a\u043e\u043d\u0446\u0435\u043f\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-b12cfa0a6432f8171149ec0139d259ce_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-4\\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<p> \u0418\u043c\u0435\u0439\u0442\u0435 \u0432 \u0432\u0438\u0434\u0443, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u0441\u0435\u0433\u0434\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0438\u0441\u043b\u043e, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0441\u043e\u043f\u0440\u043e\u0432\u043e\u0436\u0434\u0430\u0435\u0442 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0443\u044e x, \u043a\u043e\u0433\u0434\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0433\u043e \u0447\u043b\u0435\u043d\u0430 \u0438\u043b\u0438, \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0435\u0441\u043b\u0438 \u0443 \u043d\u0435\u0435 \u0435\u0441\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u0438\u043d \u0447\u043b\u0435\u043d \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440:<\/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-01c42c8e73ed47d26a090c027af24e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=8x\\quad\\longrightarrow\\quad f'(x)=8\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"223\" 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 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0431\u0435\u0437 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439, \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u0447\u0438\u0441\u043b\u043e. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-de-una-funcion-lineal\"><\/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 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0414\u0430\u043b\u0435\u0435 \u043c\u044b \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u041f\u0443\u0441\u0442\u044c <em>f \u2014<\/em> \u043b\u044e\u0431\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\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-370811a2aa0db8d9ec651bc54ec64e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=Ax+B\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"117\" 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> \u0418\u0442\u0430\u043a, \u0435\u0441\u043b\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0434\u043b\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82bb6155f8feedee8ffd37d7d721be41_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{A(a+h)+B-(A\\cdot a+B)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"456\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> \u0420\u0430\u0441\u043a\u0440\u044b\u0432\u0430\u0435\u043c \u0441\u043a\u043e\u0431\u043a\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-fad6e047e98d5201667c8605457c08f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\frac{Aa+Ah+B-Aa-B}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0414\u0435\u0439\u0441\u0442\u0432\u0443\u0435\u043c \u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\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-a65d5b69a49d803b5347d019191a4500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=\\frac{Ah}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"88\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0418 \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0443\u043f\u0440\u043e\u0449\u0430\u0435\u043c \u0434\u0440\u043e\u0431\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-33d6b2531eeda784111d43aca63830d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(a)=A\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435, \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 \u0440\u0430\u0432\u043d\u0430 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0443 \u043f\u0440\u0438 \u0447\u043b\u0435\u043d\u0435 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0432 \u043b\u044e\u0431\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432\u044b\u0432\u0435\u0434\u0435\u043d\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-de-funciones-lineales\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<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 \u043b\u0438\u043d\u0435\u0439\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-7eaaec94975c0a6f735ed64a9f4c8559_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ f(x)=2x-25\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" 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-7b6d868f61cd6a9508bd6d32040c4b0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\ f(x)=x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" 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-558f5203bb08cc856a3b3f6e5ba06880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ f(x)=-9x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" 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-dc3b5146a38b0ca48d55e02fe3318f07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)}\\ f(x)=\\cfrac{1}{2}x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"136\" 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-47708f79ca9b8e2aef23d88e5137467a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)}\\ f(x)=5x\" 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-198f38dc1105d5d3a1787a414f5b1619_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)}\\ f(x)=\\sqrt{7}x+\\frac{3}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"147\" style=\"vertical-align: -6px;\"><\/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>\u043f\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\"> \u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043f\u0440\u043e\u0441\u0442\u043e \u0438\u0441\u043a\u043b\u044e\u0447\u0438\u0442\u0435 \u0438\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u044b\u0439 \u0447\u043b\u0435\u043d \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0443\u044e, \u0447\u0442\u043e\u0431\u044b \u043e\u0441\u0442\u0430\u043b\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0433\u043e \u0447\u043b\u0435\u043d\u0430. \u0415\u0449\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-162a6c1b0989828157ac2bba886b4dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)}\\ f'(x)=2\" 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-7e751128f71b2780e6c74982ba17b8da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)}\\ f'(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" 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-745a8ca29575777f5ed665282b33ba5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)}\\ f'(x)=-9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-851faa652678a22b7aa681ef83544459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)}\\ f'(x)=\\cfrac{1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" 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-4a2874e7133b50fc9e7dd628a35296a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)}\\ f'(x)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" 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-1887bdd187bb5bcf860a6a8692de2660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)}\\ f'(x)=\\sqrt{7}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0425\u043e\u0442\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0434\u0440\u043e\u0431\u0438 \u0438\u043b\u0438 \u043a\u043e\u0440\u043d\u0438, \u0432\u044b\u0432\u043e\u0434 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0442\u0430\u043a\u0438\u043c \u0436\u0435 \u043e\u0431\u0440\u0430\u0437\u043e\u043c.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c, \u0447\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u0430 \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. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u0440\u0435\u0448\u0430\u0435\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u0443\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439. \u0412\u044b \u0434\u0430\u0436\u0435 \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \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\u044b\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \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? \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 \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 &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%bb%d0%b8%d0%bd%d0%b5%d0%b8%d0%bd%d0%be%d0%b8-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/\"> <span class=\"screen-reader-text\">\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> \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-381","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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