{"id":39,"date":"2023-09-17T11:00:46","date_gmt":"2023-09-17T11:00:46","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d8%ad%d8%a7%d8%b5%d9%84-%d8%a7%d9%84%d9%82%d8%b3%d9%85%d8%a9\/"},"modified":"2023-09-17T11:00:46","modified_gmt":"2023-09-17T11:00:46","slug":"%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d8%ad%d8%a7%d8%b5%d9%84-%d8%a7%d9%84%d9%82%d8%b3%d9%85%d8%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d8%ad%d8%a7%d8%b5%d9%84-%d8%a7%d9%84%d9%82%d8%b3%d9%85%d8%a9\/","title":{"rendered":"\u0645\u0634\u062a\u0642 \u0645\u0646 \u0627\u0644\u062d\u0627\u0635\u0644 (\u0623\u0648 \u0627\u0644\u0642\u0633\u0645\u0629)"},"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\u0633\u062a\u062e\u0644\u0627\u0635 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0642\u0633\u0645\u0629) \u0645\u0646 \u062f\u0627\u0644\u062a\u064a\u0646. \u0633\u062a\u062c\u062f \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u062e\u0627\u0631\u062c \u0642\u0633\u0645\u0629 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0648\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0642\u0633\u0645\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0645\u0627\u0631\u064a\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-un-cociente\"><\/span> \u0635\u064a\u063a\u0629 \u0644\u0645\u0634\u062a\u0642\u0629 \u062d\u0627\u0635\u0644 \u0627\u0644\u0642\u0633\u0645\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0645\u0634\u062a\u0642\u0629 \u0645\u0639\u0627\u0645\u0644 (\u0623\u0648 \u0642\u0633\u0645\u0629) \u0627\u0644\u062f\u0648\u0627\u0644<\/strong> \u0645\u0637\u0627\u0628\u0642\u0629 \u0644\u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u0628\u0633\u0637 \u0628\u0648\u0627\u0633\u0637\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0642\u0627\u0645 \u0623\u0642\u0644 \u0645\u0646 \u062f\u0627\u0644\u0629 \u0627\u0644\u0628\u0633\u0637 \u0628\u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0642\u0627\u0645 \u0645\u0642\u0633\u0648\u0645\u0629 \u0639\u0644\u0649 \u0645\u0631\u0628\u0639 \u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0642\u0627\u0645 \u0627\u0644\u0623\u0639\u0644\u0649. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-quotient-de-division-derivee.webp\" alt=\"\u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0642\u0633\u0645\u0629 \u0623\u0648 \u062d\u0627\u0635\u0644 \u0627\u0644\u0642\u0633\u0645\u0629\" class=\"wp-image-2194\" width=\"326\" height=\"304\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0639\u0646\u062f\u0645\u0627 \u0646\u0637\u0628\u0642 \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0642\u0633\u0645\u0629) \u0644\u0627 \u064a\u0632\u0627\u0644 \u0644\u062f\u064a\u0646\u0627 \u0643\u0633\u0631 \u0628\u0639\u062f \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642. \u0644\u0643\u0646\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0644\u062f\u064a\u0646\u0627 \u0641\u064a \u0627\u0644\u0628\u0633\u0637 \u0639\u0645\u0644\u064a\u062a\u064a \u0636\u0631\u0628 \u0648\u0637\u0631\u062d\u060c \u0648\u0627\u0644\u0645\u0642\u0627\u0645 \u0645\u0631\u0641\u0648\u0639 \u0644\u0644\u0623\u0633 \u0627\u062b\u0646\u064a\u0646. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-cocientes\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0642\u0633\u0645\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0642\u062f \u0631\u0623\u064a\u0646\u0627 \u0644\u0644\u062a\u0648 \u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u062e\u0627\u0631\u062c \u0642\u0633\u0645\u0629 \u062f\u0627\u0644\u062a\u064a\u0646\u060c \u0648\u0633\u0646\u0642\u0648\u0645 \u0628\u0639\u062f \u0630\u0644\u0643 \u0628\u062d\u0644 \u0639\u062f\u0629 \u0623\u0645\u062b\u0644\u0629 \u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a. \u062a\u0630\u0643\u0631\u060c \u0625\u0630\u0627 \u0643\u0646\u062a \u0644\u0627 \u062a\u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u062d\u0627\u0635\u0644 \u0627\u0644\u0648\u0638\u064a\u0641\u064a\u060c \u064a\u0645\u0643\u0646\u0643 \u0623\u0646 \u062a\u0633\u0623\u0644\u0646\u0627 \u0641\u064a \u0642\u0633\u0645 \u0627\u0644\u062a\u0639\u0644\u064a\u0642\u0627\u062a.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 1<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0646\u0634\u062a\u0642 \u062f\u0627\u0644\u0629 \u0645\u062d\u062a\u0645\u0644\u0629 \u0645\u0642\u0633\u0648\u0645\u0629 \u0639\u0644\u0649 \u062f\u0627\u0644\u0629 \u0645\u062b\u0644\u062b\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-9d260d4cdca9f28e43607a9c1e7b3404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{3x^2+4x}{\\text{sen}(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"128\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0642\u0633\u0645\u0629 \u0648\u0638\u064a\u0641\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646 \u0647\u064a \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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u0646\u062d\u062a\u0627\u062c \u0623\u0648\u0644\u0627\u064b \u0625\u0644\u0649 \u062d\u0633\u0627\u0628 \u0645\u0634\u062a\u0642\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u062d\u062f\u0629: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-21\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\" style=\";text-align:right;direction:rtl\">\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-24719cd47158514d54e16f4994a1c2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (3x^2+4x)=6x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"180\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\" style=\";text-align:right;direction:rtl\">\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-093fb274a2a393453833ed572dc1bc62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\text{sen}(2x)=2\\text{cos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"171\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627 \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-65ce4673f3ad5a4c09a9b2e7c611821d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{3x^2+4x}{\\text{sen}(2x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{(6x+4)\\cdot\\text{sen}(2x)-(3x^2+4x)\\cdot 2\\text{cos}(2x)}{\\text{sen}^2(2x)}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"380\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0633\u0646\u062c\u062f \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062b\u0627\u0628\u062a \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \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-e7d5ddfdf95f11b94783ca40437e371a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{10}{x^2+3x-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"150\" style=\"vertical-align: -14px;\"><\/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 \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0633\u0645\u0629 \u062f\u0627\u0644\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646 \u0647\u064a \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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0646\u062d\u0633\u0628 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0628\u0633\u0637 \u0648\u0627\u0644\u0645\u0642\u0627\u0645 \u0628\u0634\u0643\u0644 \u0645\u0646\u0641\u0635\u0644: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-24\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\" style=\";text-align:right;direction:rtl\">\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-191c03d69e261059308133b99f87bf1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 10=0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\" style=\";text-align:right;direction:rtl\">\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-c63da81dbf763b0a24cf929aef024c51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^2+3x-9)=2x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"201\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062c\u062f \u0645\u0634\u062a\u0642\u0629 \u0642\u0633\u0645\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\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-8f8bdea77dc91b1aff40695511593e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{10}{x^2+3x-9}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{0\\cdot (x^2+3x-9)-10\\cdot (2x+3)}{\\left(x^2+3x-9\\right)^2}=\\cfrac{-20x+30}{\\left(x^2+3x-9\\right)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"441\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u0635\u064a\u063a\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u0645\u0628\u0627\u0634\u0631 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u062b\u0627\u0628\u062a \u0641\u064a \u0627\u0644\u0628\u0633\u0637 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u062f\u0627\u0644\u0629\u060c \u0644\u0623\u0646 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062b\u0627\u0628\u062a \u062a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 0. \u0644\u0630\u0644\u0643\u060c \u0633\u062a\u0643\u0648\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0635\u062d\u064a\u062d\u0629 \u062f\u0627\u0626\u0645\u064b\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-1f0bd615634f5205f91674f96f5c2514_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}z(x)=\\cfrac{k}{f(x)} \\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{-k\\cdot f'(x)}{\\bigl(f(x)\\bigr)^2}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062a\u0645\u0631\u064a\u0646\u060c \u0633\u0648\u0641 \u0646\u0634\u062a\u0642 \u062e\u0627\u0631\u062c \u0642\u0633\u0645\u0629 \u0643\u062b\u064a\u0631\u062a\u064a \u0627\u0644\u062d\u062f\u0648\u062f:<\/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-59b390fee61ab3c2cbb4dc2230386658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u062d\u0644 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u064a\u062c\u0628 \u0623\u0646 \u0646\u0637\u0628\u0642 \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u062e\u0627\u0631\u062c \u0642\u0633\u0645\u0629 \u062f\u0627\u0644\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646\u060c \u0648\u0647\u064a \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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u062f\u0639\u0648\u0646\u0627 \u0646\u0648\u062c\u062f \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0628\u0633\u0637 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u0627\u0644\u0645\u0642\u0627\u0645 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-27\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\" style=\";text-align:right;direction:rtl\">\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-39e82139a124bf031f31b84007bcb923_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^3+4x^2)=3x^2+8x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"196\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\" style=\";text-align:right;direction:rtl\">\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-73db77f7639fc8b4cc305fbbb2b1cf2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (5x^2-8)=10x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"148\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0623\u0633\u0645\u0627\u0621 \u0627\u0644\u0645\u062a\u0639\u062f\u062f\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-065ad49556f264b4cfb505522ad7566b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"137\" width=\"373\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0648\u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u0643\u0633\u0631 \u0642\u062f\u0631 \u0627\u0644\u0625\u0645\u0643\u0627\u0646: <\/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-af3f7cb513883d1fa5dadca23701c19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\\\[2ex]&amp;=\\cfrac{15x^4-24x^2+40x^3-64x-10x^4-40x^3}{25x^4+64-80x^2}\\\\[2ex]&amp;=\\cfrac{5x^4-24x^2-64x}{25x^4-80x^2+64}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"379\" style=\"vertical-align: 0px;\"><\/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-de-un-cociente\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0629 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0634\u062a\u0642 \u062a\u0642\u0633\u064a\u0645\u0627\u062a \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \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-e6244d0e6cfcb8c4b82806d40cab93fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\cfrac{9x^2+5x}{6x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"154\" 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-e94071c6dc40cd4a7280be617cdddd3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\cfrac{19}{2x^2-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" 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-214e8c32a9ffb1c37f164935c3ad6bfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\cfrac{8x^3-4x^2+3x}{e^{4x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"202\" 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-a83ff4c06137279870296a80b12b0cec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\cfrac{\\text{cos}(x^2)}{\\text{sen}(6x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"144\" 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-4bed0ff9464adb5897528d5b47ed477c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\cfrac{\\ln(x^3+4)}{\\left(4x^2-3x\\right)^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"174\" 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-74ddf8caa494c9a60dcbfc9d57c90d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f(x)=\\cfrac{\\sqrt{x^2+4x}}{5^{x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"158\" style=\"vertical-align: -13px;\"><\/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-26b0af84dd46ca29727eee97380b4ca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{A) }f'(x)&amp;=\\cfrac{(18x+5)\\cdot 6x^3-(9x^2+5x)\\cdot 18x^2}{\\left(6x^3\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{108x^4+30x^3-162x^4-90x^3}{36x^6}\\\\[1.5ex]&amp;=\\cfrac{-54x^4-60x^3}{36x^6}\\\\[1.5ex]&amp;=\\cfrac{-9x-10}{6x^3}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"225\" width=\"354\" 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-97bee45dee6ebba49cd8a9822ef70308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\cfrac{-19\\cdot 4x}{\\left(2x^2-2\\right)^2}=\\cfrac{-76x}{\\left(2x^2-2\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"273\" 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-11f9c8fda61edb1ce51bd33e022a0a24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp;=\\cfrac{(24x^2-8x+3)e^{4x}-(8x^3-4x^2+3x)\\cdot 4e^{4x}}{\\left(e^{4x}\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{e^{4x}(24x^2-8x+3-32x^3+16x^2-12x)}{e^{8x}}\\\\[1.5ex]&amp;=\\cfrac{-32x^3+40x^2-20x+3}{e^{4x}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"431\" 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-da9da045ccfc03ecc1d9d44e1ea9caee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=\\cfrac{-2x\\text{sen}(x^2)\\cdot\\text{sen}(6x)-\\text{cos}(x^2)\\text{cos}(6x)\\cdot 6}{\\text{sen}^2(6x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"414\" 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-ec87daa1a463bacd5a42a1b16e826449_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) }f'(x)&amp;=\\cfrac{\\cfrac{3x^2}{x^3+4}\\cdot\\left(4x^2-3x\\right)^3-\\ln(x^3+4)\\cdot 3\\left(4x^2-3x\\right)^2\\cdot (8x-3) }{\\left(\\left(4x^2-3x\\right)^3\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{\\cfrac{3x^2}{x^3+4}\\cdot\\left(4x^2-3x\\right)^3-\\ln(x^3+4)\\cdot 3\\left(4x^2-3x\\right)^2\\cdot (8x-3) }{\\left(4x^2-3x\\right)^6}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"170\" width=\"535\" 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-bef2b22482e39cea7e82047c0d9911b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{F) }f'(x)&amp;=\\cfrac{\\cfrac{2x+4}{2\\sqrt{x^2+4x}}\\cdot 5^{x^2} - \\sqrt{x^2+4x}\\cdot 5^{x^2}\\cdot \\ln(5) \\cdot 2x }{\\left(5^{x^2}\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{\\cfrac{2x+4}{2\\sqrt{x^2+4x}}\\cdot 5^{x^2} - \\sqrt{x^2+4x}\\cdot 5^{x^2}\\cdot \\ln(5) \\cdot 2x }{5^{2x^2}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"155\" width=\"424\" 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-derivada-de-un-cociente\"><\/span> \u0645\u0638\u0627\u0647\u0631\u0629 \u0645\u0634\u062a\u0642 \u0645\u0646 \u0627\u0644\u062d\u0627\u0635\u0644<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u0646\u0648\u0636\u062d \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0642\u0633\u0645\u0629. \u0648\u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0633\u0648\u0641 \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0639\u0627\u0645 \u0644\u0644\u0645\u0634\u062a\u0642\u0629\u060c \u0648\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-dc1699622d128f888c1f20599aeccf60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"219\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0639 <em>z<\/em> \u064a\u0643\u0648\u0646 \u062a\u0642\u0633\u064a\u0645\u064b\u0627 \u0644\u0648\u0638\u064a\u0641\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646:<\/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-83357f61a7cd6587a3fd5e5348b056fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=\\cfrac{f(x)}{g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"94\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646 \u0641\u0625\u0646 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 <em>z<\/em> \u0627\u0644\u062a\u064a \u062a\u0637\u0628\u0642 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0633\u062a\u0643\u0648\u0646:<\/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-db6545eb9e109966a362acf510f101a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\cfrac{f(x+h)}{g(x+h)}-\\cfrac{f(x)}{g(x)}}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"223\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0644 \u0637\u0631\u062d \u0627\u0644\u0643\u0633\u0648\u0631 \u0645\u0646 \u0628\u0633\u0637 \u0627\u0644\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-f9ec617a63f72bd4215ccb2b2998525e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\cfrac{f(x+h)\\cdot g(x)}{g(x+h)\\cdot g(x)}-\\cfrac{f(x)\\cdot g(x+h)}{g(x)\\cdot g(x+h)}}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"347\" style=\"vertical-align: -13px;\"><\/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-f8a9e6382fd7033298df2e7955ccd9fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x)-f(x)\\cdot g(x+h)}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"343\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0646 \u0625\u0636\u0627\u0641\u0629 \u062d\u062f \u0627\u0644\u062c\u0645\u0639 \u0648\u0627\u0644\u0637\u0631\u062d \u0625\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0627 \u064a\u063a\u064a\u0631 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629. \u0644\u0630\u0644\u0643 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0625\u0644\u0649 \u0627\u0644\u062e\u0637\u0648\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-8581512accedfadade2e1bbbeec84855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x)\\color{orange}\\bm{-f(x)\\cdot g(x)}\\color{black}-f(x)\\cdot g(x+h)\\color{orange}\\bm{+f(x)\\cdot g(x)}\\color{black}}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"720\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u062e\u0631\u062c \u0627\u0644\u0639\u0627\u0645\u0644 \u0627\u0644\u0645\u0634\u062a\u0631\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-b8f9b502b411bb77acebc63c00972053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{g(x)\\bigl[f(x+h)-f(x)\\bigr]-f(x)\\bigl[g(x+h)-g(x)\\bigr]}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"457\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u062f\u0639\u0646\u0627 \u0646\u0646\u0642\u0644 \u0627\u0644\u062d\u062f <em>h<\/em> \u0645\u0646 \u0627\u0644\u0645\u0642\u0627\u0645 \u0625\u0644\u0649 \u0627\u0644\u0628\u0633\u0637 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0643\u0633\u0648\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-74338b745f98dd32abeea2df50b88ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{g(x)\\cdot \\cfrac{f(x+h)-f(x)\\cdot g(x)}{h}-f(x)\\cdot\\cfrac{g(x+h)-g(x)}{h}}{g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"503\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0648\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u062a\u0637\u0628\u064a\u0642 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a:<\/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-a699ddaf78abfcfbd1aa3993b6a0b033_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}\\cfrac{f(x+h)-f(x)\\cdot g(x)}{h}-f(x)\\cdot\\lim_{h \\to 0}\\cfrac{g(x+h)-g(x)}{h}}{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"535\" style=\"vertical-align: -25px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062a\u0648\u0627\u0641\u0642 \u062d\u062f\u0648\u062f \u0627\u0644\u0628\u0633\u0637 \u0628\u062f\u0642\u0629 \u0645\u0639 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\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-8735d5a5a43fa63c27443c2fe34a1530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot f'(x)-f(x)\\cdot g'(x)}{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"257\" style=\"vertical-align: -25px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0644 \u0646\u0647\u0627\u064a\u0629 \u0645\u0642\u0627\u0645 \u0627\u0644\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-1ef05117a36f586b6c8441b829bd4c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot f'(x)-f(x)\\cdot g'(x)}{g(x)\\cdot g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"257\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u062a\u0645 \u062a\u0648\u0636\u064a\u062d \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u062d\u0627\u0635\u0644 \u062f\u0627\u0644\u062a\u064a\u0646:<\/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-85517a8cdcfda040b304fbdabe67a5fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"257\" style=\"vertical-align: -23px;\"><\/p><\/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\u0633\u062a\u062e\u0644\u0627\u0635 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0642\u0633\u0645\u0629) \u0645\u0646 \u062f\u0627\u0644\u062a\u064a\u0646. \u0633\u062a\u062c\u062f \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u062e\u0627\u0631\u062c \u0642\u0633\u0645\u0629 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0648\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0642\u0633\u0645\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0645\u0627\u0631\u064a\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629. \u0635\u064a\u063a\u0629 \u0644\u0645\u0634\u062a\u0642\u0629 \u062d\u0627\u0635\u0644 \u0627\u0644\u0642\u0633\u0645\u0629 \u0645\u0634\u062a\u0642\u0629 \u0645\u0639\u0627\u0645\u0644 (\u0623\u0648 \u0642\u0633\u0645\u0629) \u0627\u0644\u062f\u0648\u0627\u0644 \u0645\u0637\u0627\u0628\u0642\u0629 \u0644\u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u0628\u0633\u0637 \u0628\u0648\u0627\u0633\u0637\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0642\u0627\u0645 \u0623\u0642\u0644 \u0645\u0646 \u062f\u0627\u0644\u0629 \u0627\u0644\u0628\u0633\u0637 \u0628\u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d8%ad%d8%a7%d8%b5%d9%84-%d8%a7%d9%84%d9%82%d8%b3%d9%85%d8%a9\/\"> <span class=\"screen-reader-text\">\u0645\u0634\u062a\u0642 \u0645\u0646 \u0627\u0644\u062d\u0627\u0635\u0644 (\u0623\u0648 \u0627\u0644\u0642\u0633\u0645\u0629)<\/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-39","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0645\u0634\u062a\u0642 \u0627\u0644\u0642\u0633\u0645\u0629 (\u0627\u0644\u0642\u0633\u0645\u0629): \u0627\u0644\u0635\u064a\u063a\u0629 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629<\/title>\n<meta name=\"description\" content=\"\u0646\u0648\u0636\u062d \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629 (\u0623\u0648 \u0627\u0644\u0642\u0633\u0645\u0629) \u0645\u0646 \u062f\u0627\u0644\u062a\u064a\u0646. \u0633\u062a\u062c\u062f \u0647\u0646\u0627\u0643 \u0627\u0644\u0635\u064a\u063a\u0629 \u0648\u0627\u0644\u062a\u062f\u0631\u064a\u0628\u0627\u062a \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0645\u0634\u062a\u0642\u0627\u062a \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629.\" \/>\n<meta name=\"robots\" content=\"index, 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