{"id":387,"date":"2023-07-03T16:46:24","date_gmt":"2023-07-03T16:46:24","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%84%d8%a7%d8%b1%d9%83%d9%88%d8%b3%d9%8a%d9%86\/"},"modified":"2023-07-03T16:46:24","modified_gmt":"2023-07-03T16:46:24","slug":"%d9%85%d8%b4%d8%aa%d9%82-%d9%84%d8%a7%d8%b1%d9%83%d9%88%d8%b3%d9%8a%d9%86","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%84%d8%a7%d8%b1%d9%83%d9%88%d8%b3%d9%8a%d9%86\/","title":{"rendered":"\u0645\u0634\u062a\u0642 \u0645\u0646 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0646\u0648\u0636\u062d \u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u0633\u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u062d\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0631\u0636 \u0644\u0643 \u0625\u062b\u0628\u0627\u062a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0627\u0644\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=\"%c2%bfcual-es-la-derivada-del-arcocoseno\"><\/span> \u0645\u0627 \u0647\u0648 \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 x \u0647\u0648 \u0633\u0627\u0644\u0628 \u0648\u0627\u062d\u062f \u0639\u0644\u0649 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u0644\u0648\u0627\u062d\u062f \u0646\u0627\u0642\u0635 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-08ccbc72f9a1b83be4c2d4ce41e7f10e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u062b\u0645\u060c <strong>\u0641\u0625\u0646 \u0645\u0634\u062a\u0642\u0629 \u0642\u0648\u0633 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629<\/strong> \u064a\u0633\u0627\u0648\u064a \u0646\u0627\u0642\u0635 \u062d\u0627\u0635\u0644 \u0645\u0634\u062a\u0642\u0629 \u062a\u0644\u0643 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u0644\u0648\u0627\u062d\u062f \u0646\u0627\u0642\u0635 \u062a\u0631\u0628\u064a\u0639 \u062a\u0644\u0643 \u0627\u0644\u062f\u0627\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 u \u0628\u0640 x \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629. \u0644\u0630\u0627\u060c \u0644\u062a\u0644\u062e\u064a\u0635\u060c \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0639\u0643\u0633\u064a \u0647\u064a: <\/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\/derive-arc-cosinus.webp\" alt=\"\u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\" class=\"wp-image-1973\" width=\"432\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0648\u0633\u064a\u0646 \u062a\u0634\u0628\u0647 <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0645\u0634\u062a\u0642-\u0644\u0627\u0631\u0643\u0648\u0632\u064a\u0646\/\">\u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646<\/a><\/span> \u060c \u0648\u0644\u0643\u0646 \u0628\u0625\u0636\u0627\u0641\u0629 \u0633\u0627\u0644\u0628 \u0642\u0628\u0644\u0647. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocoseno\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0639\u0631\u0641\u0629 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 \u0623\u0631\u0643\u0648\u0633\u064a\u0646\u060c \u0633\u0646\u062d\u0644\u0644 \u0627\u0644\u0622\u0646 \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 \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 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \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-arcocoseno-de-2x\"><\/span> \u0645\u062b\u0627\u0644 1: \u0645\u0634\u062a\u0642 \u0645\u0646 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 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-c913be328da0f829a3545ccf101e15e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u062d\u0644 \u0645\u0634\u062a\u0642\u0629 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\u060c \u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u062a\u0647:<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642 2x \u0647\u0648 2\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 2x \u0647\u0648 \u0633\u0627\u0644\u0628 2 \u0639\u0644\u0649 \u062c\u0630\u0631 \u0648\u0627\u062d\u062f \u0646\u0627\u0642\u0635 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-cf892a94fcba0edb3ae5c4d8ff013899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\sqrt{1-(2x)^2}}=-\\cfrac{2}{\\sqrt{1-4x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"576\" 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-2-derivada-del-arcocoseno-de-x-al-cuadrado\"><\/span> \u0645\u062b\u0627\u0644 2: \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \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-b2f6ac6474aa61a7eddba4bb79a45ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0637\u0628\u0642 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0648\u0633\u064a\u0646 \u0645\u0639 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0634\u062a\u0642:<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0627 \u0623\u0646 \u0645\u0634\u062a\u0642 \u0627\u0644\u062f\u0627\u0644\u0629 x <sup>2<\/sup> \u0647\u0648 2x\u060c \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 x \u0623\u0633 2 \u0647\u0648: <\/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-e9180f04fd27262ca57f4b648c3b6b9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\sqrt{1-\\left(x^2\\right)^2}}=-\\cfrac{2x}{\\sqrt{1-x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"565\" style=\"vertical-align: -30px;\"><\/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-arcocoseno-de-un-logaritmo\"><\/span> \u0645\u062b\u0627\u0644 3: \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645<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-d172240febea273fb3978225f13eebad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062f\u0627\u0644\u0629 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u062b\u0627\u0644 \u0647\u064a \u062f\u0627\u0644\u0629 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u0623\u0631\u0643\u0648\u0633\u064a\u0646 \u0648\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0637\u0628\u064a\u0639\u064a\u060c \u0644\u0630\u0644\u0643 \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0644\u0627\u0634\u062a\u0642\u0627\u0642\u0647\u0627.<\/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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(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=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0647\u0648 \u0648\u0627\u062d\u062f \u0645\u0642\u0633\u0648\u0645 \u0639\u0644\u0649 x\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0647\u0648: <\/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-d682371fc7d064383f30416a40a4f9ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\cfrac{1}{x}}{\\sqrt{1-\\left(\\ln(x)\\right)^2}}=\\cfrac{1}{x\\sqrt{1-\\ln^2(x)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"582\" style=\"vertical-align: -30px;\"><\/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-arcocoseno\"><\/span> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0645\u0634\u062a\u0642\u0627\u062a \u0623\u0631\u0643\u0648\u0633\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0634\u062a\u0642 \u0648\u0638\u0627\u0626\u0641 \u0623\u0631\u0643\u0648\u0633\u064a\u0646 \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-35e2715201a91cea5d5a914619695b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arccos}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" 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-a2bc15a65a4f4e6c42effc3e21437657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arccos}(x^3+6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-38ed3b9ec0b9a3cb6443dec0c6afb6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arccos}^3\\left(e^{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" 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-766af35119810145dd3589fab05d2f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arccos}\\left(\\log_3(x^3)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" 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-ce6b5d78ea798a70c51759cce27e5b25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arccos}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"181\" style=\"vertical-align: -7px;\"><\/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-79dbfad4db01cc46534b4875a7a8c905_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=-\\cfrac{7}{\\sqrt{1-(7x)^2}}=-\\cfrac{7}{\\sqrt{1-49x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"314\" 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-fd07daef79650fcb34116e266aee09fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=-\\cfrac{3x^2+6}{\\sqrt{1-(x^3+6x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"233\" 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-0ffd255c55afc3967dc250bc63741575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }\\displaystyle f'(x)&amp;=3\\text{arccos}^2\\left(e^{3x}\\right)\\cdot \\left(-\\frac{3e^{3x}}{\\sqrt{1-\\left(e^{3x}\\right)^2}}\\right)\\\\[1.5ex] &amp;=-\\cfrac{9\\text{arccos}^2\\left(e^{3x}\\right)\\cdot e^{3x}}{\\sqrt{1-e^{6x}}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"131\" width=\"346\" style=\"vertical-align: 0px;\"><\/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-ec25311613f0552bbc52d2d15581d3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp;=-\\cfrac{1}{\\sqrt{1-\\left(\\log_3(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 3}\\\\[1.5ex] &amp;=-\\cfrac{1}{x\\cdot \\ln 3\\cdot \\sqrt{1-\\log_3^2(3x)}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"312\" style=\"vertical-align: 0px;\"><\/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-d1a362c38a56084dec3c6ebbccba9ab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) } f'(x)&amp; =-\\cfrac{1}{\\sqrt{1-\\left(\\sqrt{4x}\\right)^2}}\\cdot \\cfrac{4}{2\\sqrt{4x}}\\\\[1.5ex] &amp;=-\\cfrac{2}{\\sqrt{1-4x}\\cdot 2\\sqrt{x}}\\\\[1.5ex] &amp;=-\\cfrac{1}{\\sqrt{x-4x^2}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"184\" width=\"267\" style=\"vertical-align: 0px;\"><\/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-arcocoseno\"><\/span> \u0625\u062b\u0628\u0627\u062a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0642\u0633\u0645\u060c \u0633\u0646\u0648\u0636\u062d \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0648\u0633 \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-0a3001135fdded9698f51b8a683036c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arccos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627\u064b\u060c \u0646\u0642\u0648\u0645 \u0628\u062a\u062d\u0648\u064a\u0644 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0642\u0648\u0633\u064a \u0625\u0644\u0649 \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-32b94bb993d1256aa9088d9bffbb0941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{cos}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u0646\u062a\u062c \u0627\u0644\u0622\u0646 \u0637\u0631\u0641\u064a \u0627\u0644\u0645\u0633\u0627\u0648\u0627\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-e5f229f3e26b190eca429017bd78dba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=-\\text{sen}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0648\u0636\u062d \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-b2c2f95f5c7999d81cd10976320a7413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\text{sen}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0647\u0648\u064a\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u062a\u063a\u064a\u064a\u0631 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0625\u0644\u0649 \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-9af2ef5387e227b363035275ba0777e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{sen}(y)=\\sqrt{1-\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"390\" style=\"vertical-align: -6px;\"><\/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-3c3807ba3700aac7694b04356a9a25d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"157\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646 \u0623\u0639\u0644\u0627\u0647 \u0627\u0633\u062a\u0646\u062a\u062c\u0646\u0627 \u0623\u0646 x \u064a\u0633\u0627\u0648\u064a \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 y\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u062a\u0638\u0644 \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-8c3b21ba43e58ec763ab27498aa4fb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"117\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0647\u0643\u0630\u0627 \u0648\u0635\u0644\u0646\u0627 \u0625\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062e\u0627\u0635 \u0628\u0645\u0634\u062a\u0642\u0629 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\u060c \u062d\u064a\u062b \u062a\u0645 \u062a\u0648\u0636\u064a\u062d \u0635\u064a\u063a\u062a\u0647.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0646\u0648\u0636\u062d \u0647\u0646\u0627 \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u0633\u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u062d\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0639\u0631\u0636 \u0644\u0643 \u0625\u062b\u0628\u0627\u062a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0627\u0644\u0623\u0631\u0643\u0648\u0633\u064a\u0646. \u0645\u0627 \u0647\u0648 \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\u061f \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 x \u0647\u0648 \u0633\u0627\u0644\u0628 \u0648\u0627\u062d\u062f \u0639\u0644\u0649 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u0644\u0648\u0627\u062d\u062f \u0646\u0627\u0642\u0635 x \u062a\u0631\u0628\u064a\u0639. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%84%d8%a7%d8%b1%d9%83%d9%88%d8%b3%d9%8a%d9%86\/\"> <span class=\"screen-reader-text\">\u0645\u0634\u062a\u0642 \u0645\u0646 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &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-387","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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