{"id":386,"date":"2023-07-03T16:55:30","date_gmt":"2023-07-03T16:55:30","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%b2%d9%8a%d9%86\/"},"modified":"2023-07-03T16:55:30","modified_gmt":"2023-07-03T16:55:30","slug":"%d9%85%d8%b4%d8%aa%d9%82-%d9%84%d8%a7%d8%b1%d9%83%d9%88%d8%b2%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%b2%d9%8a%d9%86\/","title":{"rendered":"\u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0646\u0634\u0631\u062d \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629. \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\u062f\u0648\u0627\u0644 \u0648\u064a\u0645\u0643\u0646\u0643 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u062a\u0634\u0627\u0647\u062f \u0623\u064a\u0636\u064b\u0627 \u0639\u0631\u0636\u064b\u0627 \u062a\u0648\u0636\u064a\u062d\u064a\u064b\u0627 \u0644\u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0623\u0631\u0643\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-arcoseno\"><\/span> \u0645\u0627 \u0647\u0648 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646\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 \u0627\u0644\u062c\u064a\u0628 \u0644\u0640 x \u0647\u0648 \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-924f0591661727fa46ea5f69bff39401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 <strong>\u0645\u0634\u062a\u0642\u0629 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629<\/strong> \u064a\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 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u0644\u0648\u0627\u062d\u062f \u0646\u0627\u0642\u0635 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646\u0637\u0642\u064a\u0627\u060c \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0623\u0648\u0644\u0649. <\/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-de-larcosine.webp\" alt=\"\u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646\" class=\"wp-image-1952\" width=\"403\" height=\"304\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u0630\u0643\u0631 \u0623\u0646 \u0623\u0631\u0643\u0633\u064a\u0646 \u0647\u064a \u062f\u0627\u0644\u0629 \u0639\u0643\u0633\u064a\u0629 \u0644\u0644\u062c\u064a\u0628\u060c \u0648\u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628 \u062a\u0633\u0645\u0649 \u0623\u064a\u0636\u064b\u0627 \u062c\u064a\u0628 \u0627\u0644\u062c\u064a\u0628 \u0627\u0644\u0639\u0643\u0633\u064a. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcoseno\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0627\u0644\u0627\u0637\u0644\u0627\u0639 \u0639\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0623\u0631\u0643\u0633\u064a\u0646\u060c \u0633\u0646\u0634\u0631\u062d \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\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-arcoseno-de-2x\"><\/span> \u0645\u062b\u0627\u0644 1: \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062c\u064a\u0628 \u0644\u0640 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-61368fb29b840d3583de92c8e6202006_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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\"> \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642 \u062f\u0627\u0644\u0629 \u0623\u0631\u0643\u0633\u064a\u0646\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0644\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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646 \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\u062c\u064a\u0628 2x \u0647\u0648 2 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \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-b0282aa3f00df6b3bd1046fff94fa586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"550\" 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-arcoseno-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-a4962743c0667c1443d315dd330bf3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"137\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646 \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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062f\u0627\u0644\u0629 x <sup>2<\/sup> \u0647\u064a \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629\u060c \u0644\u0630\u0627 \u0641\u0625\u0646 \u0645\u0634\u062a\u0642\u062a\u0647\u0627 \u0647\u064a 2x. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u062c\u064a\u0628 \u0644\u0640 x \u0645\u0631\u0641\u0648\u0639\u064b\u0627 \u0644\u0644\u0642\u0648\u0629 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-60a677a7b7ca12bf048e6d20aca7b122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"538\" 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-arcoseno-de-ex\"><\/span> \u0645\u062b\u0627\u0644 3: \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 e <sup>x<\/sup><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-0843fbec2d0e53f9f16fd8e704af9763_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(e^x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/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\u0631\u0643\u0628\u0629\u060c \u0644\u0630\u0627 \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u062a\u0637\u0628\u064a\u0642 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\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-cd5a61d8ff601317ce4d47d168b350e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(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=\"418\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642 e <sup>x<\/sup> \u0647\u0648 \u0646\u0641\u0633\u0647\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627 \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-e836cc1a00000f86d4f8891a12f4997d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arcsen}(e^x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{e^x}{\\sqrt{1-\\left(e^x\\right)^2}}=\\cfrac{e^x}{\\sqrt{1-e^{2x}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"542\" 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-arcoseno\"><\/span> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0633\u062a\u0646\u062a\u062c \u062f\u0648\u0627\u0644 arcsine \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-515f2956c43c783ea330e8b3addf908c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arcsen}(6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" 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-537773e0ce262d3f14bb6af61b6d5d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arcsen}(x^2-4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"203\" 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-d2ed0ca6a00694c6b35b651d9e206bbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arcsen}\\left(3x^4-6x^3+9+e^{x^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"304\" style=\"vertical-align: -11px;\"><\/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-c3b5ab58c98e35c39ea82368aebabded_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arcsen}\\left(\\log_5(3x)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"212\" 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-25cafb754c9abd936852c9884fa1d9ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arcsen}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"182\" 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-3d8fcc06d1afecc77f744ddddafc702f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=\\cfrac{6}{\\sqrt{1-(6x)^2}}=\\cfrac{6}{\\sqrt{1-36x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"287\" 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-4491410567de31ccb0be97922264ca90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\cfrac{2x-4}{\\sqrt{1-(x^2-4x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"219\" 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-b436dbd761b2261168c506e7e2e0d246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f'(x)=\\cfrac{12x^3-18x^2+2x\\cdot e^{x^2}}{\\sqrt{1-(3x^4-6x^3+9+e^{x^2})^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"53\" width=\"311\" style=\"vertical-align: -21px;\"><\/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-57f2d6846bdde50321c1387f949d983a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=\\cfrac{1}{\\sqrt{1-\\left(\\log_5(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 5}=\\cfrac{1}{x\\cdot \\ln 5\\cdot \\sqrt{1-\\left(\\log_5(3x)\\right)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"519\" 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-0a82c0fd18a8672100ed3b79525a1028_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=\"253\" 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-arcoseno\"><\/span> \u0625\u062b\u0628\u0627\u062a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0646\u0646\u062a\u0642\u0644 \u0625\u0644\u0649 \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0648\u0633 \u0627\u0644\u062c\u064a\u0628.<\/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-139a7a695d83cf004f32f983b10bde10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arcsen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" 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 \u0642\u0648\u0633 \u0627\u0644\u062c\u064a\u0628 \u0625\u0644\u0649 \u062c\u064a\u0628:<\/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-443f95e83265d63f8d88d8782d014011_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{sen}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0641\u0631\u0642 \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-1a653163fb7285dbfafcbaaa4b80031e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\text{cos}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" 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-ac9839cbaf86cd3bcd2020ae70eb57e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\text{cos}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"86\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0646\u0637\u0628\u0642 \u0627\u0644\u0647\u0648\u064a\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\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-d5c5551414baf4b4a0f28a4eac057ae2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{cos}(y)=\\sqrt{1-\\text{sen}^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-0535c541ff9c3a80c457aae33b359bbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\sqrt{1-\\text{sen}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"144\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0643\u0645\u0627 \u0627\u0633\u062a\u0646\u062a\u062c\u0646\u0627 \u0623\u0639\u0644\u0627\u0647 \u0623\u0646 x \u0643\u0627\u0646\u062a \u0645\u0643\u0627\u0641\u0626\u0629 \u0644\u062c\u064a\u0628 y\u060c \u062a\u0638\u0644 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0643\u0645\u0627 \u064a\u0644\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-6fafe005791d06de3e64e76eda0ac194_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=\"103\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0627 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u062d\u0635\u0644\u0646\u0627 \u0639\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u062f\u0627\u0644\u0629 \u0623\u0631\u0643\u0633\u064a\u0646\u060c \u0644\u0630\u0644\u0643 \u064a\u0638\u0647\u0631 \u0623\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u0642\u062f \u062a\u0645 \u0627\u0633\u062a\u064a\u0641\u0627\u0621\u0647\u0627.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0646\u0634\u0631\u062d \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0642\u0648\u0633 \u062c\u064a\u0628 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629. \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\u062f\u0648\u0627\u0644 \u0648\u064a\u0645\u0643\u0646\u0643 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u062a\u0634\u0627\u0647\u062f \u0623\u064a\u0636\u064b\u0627 \u0639\u0631\u0636\u064b\u0627 \u062a\u0648\u0636\u064a\u062d\u064a\u064b\u0627 \u0644\u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0623\u0631\u0643\u0633\u064a\u0646. \u0645\u0627 \u0647\u0648 \u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646\u061f \u0645\u0634\u062a\u0642 \u0642\u0648\u0633 \u0627\u0644\u062c\u064a\u0628 \u0644\u0640 x \u0647\u0648 \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. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 &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%b2%d9%8a%d9%86\/\"> <span class=\"screen-reader-text\">\u0645\u0634\u062a\u0642 \u0623\u0631\u0643\u0633\u064a\u0646<\/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-386","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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