{"id":35,"date":"2023-09-17T11:02:19","date_gmt":"2023-09-17T11:02:19","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82%d8%a9-%d8%b8%d9%84-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-1\/"},"modified":"2023-09-17T11:02:19","modified_gmt":"2023-09-17T11:02:19","slug":"%d9%85%d8%b4%d8%aa%d9%82%d8%a9-%d8%b8%d9%84-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-1","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82%d8%a9-%d8%b8%d9%84-%d8%a7%d9%84%d8%b2%d8%a7%d9%88%d9%8a%d8%a9-1\/","title":{"rendered":"\u0645\u0634\u062a\u0642 \u0645\u0646 \u0642\u0648\u0633 \u0627\u0644\u0638\u0644"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629\u060c \u0633\u0648\u0641 \u062a\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0648\u062d\u062a\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u062d\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0637\u0628\u064a\u0629. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0631\u0636 \u0644\u0643 \u0623\u064a\u0636\u064b\u0627 \u0625\u062b\u0628\u0627\u062a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcotangente\"><\/span> \u0645\u0627 \u0647\u0648 \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u0627\u0644\u0638\u0644\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0645\u0634\u062a\u0642\u0629 \u0642\u0648\u0633 \u0627\u0644\u0638\u0644 \u0644\u0640 x \u0647\u064a \u0648\u0627\u062d\u062f \u0639\u0644\u0649 \u0648\u0627\u062d\u062f \u0632\u0627\u0626\u062f x \u062a\u0631\u0628\u064a\u0639.<\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdeb5e29b862b8b9d5bc9f4c2c747106_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{1+x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u062b\u0645\u060c \u0641\u0625\u0646 <strong>\u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u062f\u0627\u0644\u0629<\/strong> \u062a\u0633\u0627\u0648\u064a \u062d\u0627\u0635\u0644 \u0642\u0633\u0645\u0629 \u0645\u0634\u062a\u0642\u0629 \u062a\u0644\u0643 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u0648\u0627\u062d\u062f \u0632\u0627\u0626\u062f \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0630\u0643\u0648\u0631\u0629 \u062a\u0631\u0628\u064a\u0639.<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u062a\u0645 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0640 au\u060c \u0644\u0630\u0627 \u0633\u062a\u0643\u0648\u0646 \u0647\u0630\u0647 \u0647\u064a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0642\u0648\u0633\u064a \u0644\u0644\u062f\u0627\u0644\u0629 u. <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-arctangente.webp\" alt=\"\u0645\u0634\u062a\u0642\u0629 \u0645\u0646 \u0642\u0648\u0633 \u0627\u0644\u0638\u0644\" class=\"wp-image-1997\" width=\"389\" height=\"296\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0645\u0645\u0627\u0633 \u0627\u0644\u0639\u0643\u0633\u064a \u062a\u0634\u0628\u0647 \u0625\u0644\u0649 \u062d\u062f \u0643\u0628\u064a\u0631 \u0635\u064a\u063a \u0645\u0634\u062a\u0642\u0627\u062a \u0623\u0631\u0643\u0633\u064a\u0646 \u0648\u0623\u0631\u0643\u0648\u0633\u064a\u0646. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcotangente\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0639\u0631\u0641 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0637\u0628\u064a\u0629\u060c \u0633\u0646\u0634\u0631\u062d \u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u062f\u0629 \u0623\u0645\u062b\u0644\u0629 \u0644\u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629. \u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0623\u0633\u0647\u0644 \u0639\u0644\u064a\u0643 \u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcotangente-de-2x\"><\/span> \u0645\u062b\u0627\u0644 1: \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c8877ac889f77baa22f66d4b2568418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0637\u0628\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u062d\u0644 \u0627\u0644\u0645\u0634\u062a\u0642\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642\u0629 2x \u0647\u064a 2\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0642\u0648\u0633\u064a\u0629 \u0644\u0640 2x \u0647\u064a 2 \u0639\u0644\u0649 \u0648\u0627\u062d\u062f \u0632\u0627\u0626\u062f 2x \u062a\u0631\u0628\u064a\u0639: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2a5ff151a4471bb769c46ac896ee0ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{1+(2x)^2}}=\\cfrac{2}{1+ 4x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"518\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcotangente-de-x-al-cuadrado\"><\/span> \u0645\u062b\u0627\u0644 2: \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u0640 x \u062a\u0631\u0628\u064a\u0639<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f62897c299972bd734ffe87b6d28e84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 \u0645\u0634\u062a\u0642\u0629 \u0647\u0630\u0627 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0639\u0644\u064a\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629\u060c \u0648\u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u0627\u0644\u062f\u0627\u0644\u0629 x <sup>2<\/sup> \u0647\u0648 2x\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 x \u0645\u0631\u0641\u0648\u0639\u0629 \u0644\u0644\u0623\u0633 2 \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4518d6b8df16464b2a763eb7d736504d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{1+\\left(x^2\\right)^2}=\\cfrac{2x}{1+x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"507\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcotangente-del-seno-de-x\"><\/span> \u0645\u062b\u0627\u0644 3: \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u062c\u064a\u0628 x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-72df0a729eefc917694a84ecccd4a959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}\\bigl(\\text{sen}(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"170\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646\u0637\u0642\u064a\u0627\u060c \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0634\u062a\u0642 \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0644\u062f\u064a\u0646\u0627 \u062f\u0627\u0644\u0629 \u0645\u0631\u0643\u0628\u0629\u060c \u0644\u0630\u0627 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0644\u062d\u0633\u0627\u0628 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3897b362bb6b4681404918f45e91565_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}\\bigl(\\text{sen}(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{\\text{cos}(x)}{1+\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"482\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcotangente\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0633\u062a\u0646\u062a\u062c \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u0648\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23cb449bba097b71c6154e6bfd755940_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{arctan}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"164\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8ec295f2cfb72911775d2bc47d379e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\cfrac{\\text{arctan}(3x^4)}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"175\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e54c5dc5ee8464186009da410740df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\text{arctan}(x^5-3x^3+10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"252\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b63b4e04e749c7b7d4cfecca4391eee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arctan}^3(4x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c72a415d8c2e54870c4dc2e92344cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arctan}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"185\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4fad4c5f97c1492b8ad5df06b165d2c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{arctan}\\left(\\sqrt{x^2+2x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"227\" style=\"vertical-align: -11px;\"><\/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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong> <\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-effa4065c7c98ae655b2cc5bdf14ca07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{3x^2}{1+\\left(x^3\\right)^2}=\\cfrac{3x^2}{1+x^6}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"235\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2de05c8d708d379982abc8461f5d8706_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{12x^3}{2\\left(1+\\left(3x^4\\right)^2\\right)}=\\cfrac{6x^3}{1+9x^8}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"285\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d72faae19f9b5cd7a8d53364bcf9817a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=\\cfrac{5x^4-9x^2}{1+\\left(x^5-3x^3+10\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"248\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea7d5ff105b7432c2756cdcbf44e311b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=3\\text{arctan}^2(4x^2)\\cdot \\cfrac{8x}{1+\\left(4x^2\\right)^2}=\\cfrac{24x\\cdot\\text{arctan}^2(4x^2)}{1+16x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"453\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6eefb865fce5124f8326d122437c3124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{\\cfrac{1}{x}}{1+\\bigl(\\ln(x)\\bigr)^2}=\\cfrac{1}{x\\left(1+\\ln^2(x)\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"315\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6faff8aba659922b2cfc784a4f3dae4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{1}{1+\\left(\\sqrt{x^2+2x}\\right)^2}\\cdot \\cfrac{2x+2}{2\\sqrt{x^2+2x}}=\\cfrac{x+1}{\\left(1+x^2+2x\\right)\\sqrt{x^2+2x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"524\" style=\"vertical-align: -33px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-del-arcotangente\"><\/span>\u062a\u0648\u0636\u064a\u062d \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0634\u0645\u0627\u0644\u064a\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u062b\u0628\u062a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88c05a50eddb183a57270676d6ebc5cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arctan}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627\u064b \u0628\u062a\u062d\u0648\u064a\u0644 \u0638\u0644 \u0642\u0648\u0633\u064a \u0625\u0644\u0649 \u0645\u0645\u0627\u0633 \u0645\u0633\u062a\u0641\u064a\u062f\u064a\u0646 \u0645\u0646 \u062d\u0642\u064a\u0642\u0629 \u0623\u0646 \u0638\u0644 \u0627\u0644\u0638\u0644 \u0627\u0644\u0639\u0643\u0633\u064a \u0647\u0648 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629 \u0644\u0644\u0638\u0644:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e806041dd9dbc7cf01bb34014aa18d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{tan}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0641\u0631\u0642 \u0628\u064a\u0646 \u0637\u0631\u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca9f080338b9ab014e272f81395146ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\cfrac{1}{\\text{cos}^2(y)}\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"114\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0628\u0645\u0633\u062d \u0648&#8217;:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05c04d0ce365d8bd7848d4923038778c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\text{cos}^2(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0648\u0628\u0641\u0636\u0644 \u0627\u0644\u0647\u0648\u064a\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629\u060c \u0646\u0639\u0644\u0645 \u0623\u0646 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u064a\u0633\u0627\u0648\u064a 1. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0633\u0627\u0628\u0642 \u0625\u0644\u0649 \u0643\u0633\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34f7d2ec2a5836c843db8adea73d021f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5314e15fe7e8ff7c9155906e7725483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\text{cos}^2(y)}{1}=\\cfrac{\\text{cos}^2(y)}{\\text{sen}^2(y)+\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"252\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0633\u0645 \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0639\u0644\u0649 \u0645\u0631\u0628\u0639 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-39e03a87b9a62ab2db6a56192e44f531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\cfrac{\\text{cos}^2(y)}{\\text{cos}^2(y)}}{\\cfrac{\\text{sen}^2(y)}{\\text{cos}^2(y)}+\\cfrac{\\text{cos}^2(y)}{\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"96\" width=\"176\" style=\"vertical-align: -44px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3cf88afedfff6a5c53ffb31df510b4ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\cfrac{\\text{sen}^2(y)}{\\text{cos}^2(y)}+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"128\" style=\"vertical-align: -44px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062c\u064a\u0628 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u064a\u0633\u0627\u0648\u064a \u0627\u0644\u0638\u0644\u060c \u0644\u0630\u0644\u0643:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dbf6d65fa67f0a2161bd99ee7431f015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"124\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db914ed4a068a6dff2598b981b1682d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\text{tan}^2(y)+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"126\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0631\u0623\u064a\u0646\u0627 \u0623\u0639\u0644\u0627\u0647\u060c \u0641\u0625\u0646 \u0627\u0644\u0638\u0644 \u064a\u0643\u0627\u0641\u0626 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 x\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61292316edd6cef99a6135989713cd22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{x^2+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"88\" style=\"vertical-align: -14px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629\u060c \u0633\u0648\u0641 \u062a\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0638\u0644 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a 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