{"id":37,"date":"2023-09-17T11:01:40","date_gmt":"2023-09-17T11:01:40","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d8%a7%d9%84%d8%b7%d8%b1%d8%ad\/"},"modified":"2023-09-17T11:01:40","modified_gmt":"2023-09-17T11:01:40","slug":"%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d8%a7%d9%84%d8%b7%d8%b1%d8%ad","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d8%a7%d9%84%d8%b7%d8%b1%d8%ad\/","title":{"rendered":"\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0637\u0631\u062d"},"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 \u0637\u0631\u062d \u0627\u0644\u062f\u0648\u0627\u0644 (\u0627\u0644\u0635\u064a\u063a\u0629). \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0637\u0631\u062d \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-resta\"><\/span> \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0637\u0631\u062d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0645\u0634\u062a\u0642\u0629 \u0637\u0631\u062d \u062f\u0627\u0644\u062a\u064a\u0646 \u062a\u0633\u0627\u0648\u064a \u0637\u0631\u062d \u0645\u0634\u062a\u0642\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u062d\u062f\u0629.<\/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-2eb280531ada831cf451f6440ac3cb7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)-g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)-g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"463\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0627\u0634\u062a\u0642\u0627\u0642 \u062f\u0627\u0644\u062a\u064a\u0646 \u0645\u0646\u0641\u0635\u0644\u062a\u064a\u0646 \u062b\u0645 \u0637\u0631\u062d\u0647\u0645\u0627 \u064a\u0639\u0627\u062f\u0644 \u0637\u0631\u062d \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646 \u0623\u0648\u0644\u064b\u0627 \u062b\u0645 \u0623\u062e\u0630 \u0627\u0644\u0645\u0634\u062a\u0642\u0629. <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-d-une-soustraction-1.webp\" alt=\"\u0645\u0634\u062a\u0642 \u0645\u0646 \u0627\u0644\u0637\u0631\u062d\" class=\"wp-image-2053\" width=\"243\" height=\"243\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u062a\u0646\u0637\u0628\u0642 \u0646\u0641\u0633 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0644\u0649 \u0637\u0631\u062d \u062f\u0627\u0644\u062a\u064a\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631\u060c \u0644\u0630\u0644\u0643 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0637\u0631\u062d \u062b\u0644\u0627\u062b\u060c \u0623\u0631\u0628\u0639\u060c \u062e\u0645\u0633\u060c&#8230;\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0627\u0634\u062a\u0642\u0627\u0642 \u0643\u0644 \u0645\u0646\u0647\u0627 \u0639\u0644\u0649 \u062d\u062f\u0629 \u062b\u0645 \u0637\u0631\u062d\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-8bc282473a7f7560eebc97db66bb8f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=f(x)- g(x)- h(x)- \\dots\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex]z'(x)=f'(x)-g'(x)- h'(x)- \\dots\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u062e\u062a\u0644\u0627\u0641 \u0627\u0644\u062f\u0648\u0627\u0644 \u062a\u0634\u0628\u0647 \u0625\u0644\u0649 \u062d\u062f \u0643\u0628\u064a\u0631 \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0645\u062c\u0645\u0648\u0639.<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0645\u0634\u062a\u0642-\u0645\u0646-\u0627\u0644\u0645\u0628\u0644\u063a\/\">\u0645\u0634\u062a\u0642\u0629 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u062f\u0648\u0627\u0644<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-una-resta\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0637\u0631\u062d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0631\u0623\u064a\u0646\u0627 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u0637\u0631\u062d\u060c \u0646\u0646\u062a\u0642\u0644 \u0627\u0644\u0622\u0646 \u0625\u0644\u0649 \u062a\u062d\u0644\u064a\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 \u0644\u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0637\u0631\u062d \u0628\u0634\u0643\u0644 \u0643\u0627\u0645\u0644. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-resta-de-funciones-potenciales\"><\/span> \u0645\u062b\u0627\u0644 1: \u0645\u0634\u062a\u0642\u0629 \u0637\u0631\u062d \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629<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-ea1b9e305c4c2b69fa19c4458715aa03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-4x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642\u0629 \u0637\u0631\u062d \u062f\u0627\u0644\u062a\u064a\u0646 \u062a\u0639\u0627\u062f\u0644 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0645\u0634\u062a\u0642\u0627\u062a \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u062d\u062f\u0629. \u0644\u0630\u0644\u0643 \u0633\u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627\u064b \u0628\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-57\" 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-d80e76a954f8534d7a4229864ab4c7ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ x^3=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\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-c96360191da869602a245eff5e086e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 4x=4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"77\" 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 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627 \u0647\u0648 \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-e0227a82cee066220095b0cb8a73276f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"120\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-resta-de-funciones-distintas\"><\/span> \u0645\u062b\u0627\u0644 2: \u0645\u0634\u062a\u0642\u0629 \u0637\u0631\u062d \u062f\u0648\u0627\u0644 \u0645\u062e\u062a\u0644\u0641\u0629<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-3359936db8c2787dcb9d1c9eb1afb194_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x)-\\log_7(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"189\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 \u062f\u0648\u0627\u0644 \u0627\u0644\u0637\u0631\u062d\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0623\u0648\u0644\u0627\u064b \u0627\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u0648\u0638\u064a\u0641\u062a\u064a\u0646 \u0628\u0634\u0643\u0644 \u0645\u0646\u0641\u0635\u0644 \u062b\u0645 \u0637\u0631\u062d\u0647\u0645\u0627. <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-60\" 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-88911e0c596da5c7e5cd27ae8411eda1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ \\text{cos}(x)=-\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"158\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\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-440c15ed64920bf34bb54bc46cece0e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\log_7 (x^2)=\\cfrac{2x}{x^2\\cdot \\ln(7)}=\\cfrac{2}{x\\ln(7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"261\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0639\u062f \u0639\u0645\u0644 \u0627\u0644\u0645\u0634\u062a\u0642\u062a\u064a\u0646 \u0646\u0637\u0631\u062d\u0647\u0645\u0627 \u0628\u0646\u0641\u0633 \u0627\u0644\u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0623\u0648\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-2e37e34506772fb550148f02cbc9ebdd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\text{sen}(x)-\\cfrac{2}{x\\ln(7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"200\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-resta-al-cuadrado\"><\/span> \u0645\u062b\u0627\u0644 3: \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0637\u0631\u062d \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a<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-3fea677e30feb8612d8d9ff7108a1625_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(x^7-2x^3-9\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"178\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0644\u062f\u064a\u0646\u0627 \u062f\u0627\u0644\u0629 \u0645\u0631\u0643\u0628\u0629\u060c \u0644\u0623\u0646\u0647\u0627 \u0639\u0645\u0644\u064a\u0629 \u0637\u0631\u062d \u0628\u064a\u0646 \u062b\u0644\u0627\u062b \u062f\u0648\u0627\u0644 \u0645\u0631\u0628\u0639\u0629. \u0644\u0630\u0644\u0643 \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 \u0645\u062d\u062a\u0645\u0644\u0629 \u0648\u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0644\u062d\u0633\u0627\u0628 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0623\u0643\u0645\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-4592b6df0dc2ed15a07f4382a817372f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2\\left(x^7-2x^3-9\\right)\\cdot \\left(7x^6-6x^2\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"285\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0645\u0634\u062a\u0642-\u0645\u0646-\u0648\u0638\u064a\u0641\u0629-\u0627\u0644\u0637\u0627\u0642\u0629-\u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629\/\">\u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0642\u0648\u0629<\/a><\/span> <\/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-una-resta\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0637\u0631\u062d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0633\u062a\u0646\u062a\u062c \u0627\u0644\u0637\u0631\u062d \u0627\u0644\u062a\u0627\u0644\u064a \u0644\u0644\u0648\u0638\u0627\u0626\u0641: <\/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-554714ddbd627e6e4db47875cf74ced0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=9x^3-5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" 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-a44e7914b191221833e66b56cfb85c0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=4x^5-6x^4-x^2-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"229\" 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-d2ffe7ee4f97af710c28c149b75ee6fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\left(-3x^7-2x^5\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"196\" 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-e2a65669468838e35b6314f216c94c20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\ln(5x^2+3x)-\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"249\" 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-b2a845babbdb5c1108fb183266b265cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=8x^3-e^{5x}-\\sqrt{8x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"241\" style=\"vertical-align: -5px;\"><\/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-a7619c845d231badc6717536370242c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=27x^2-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" 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-69d4ff912fd82dfe90ff0996b1782195_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=20x^4-24x^3-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" 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-efabd300a93704ba1ef8dd75ab565c32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=4\\left(-3x^7-2x^5\\right)^3\\cdot (-21x^6-10x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"345\" 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-ef722845586f56e6fa7aff817614b6b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=\\cfrac{10x+3}{5x^2+3x}-\\bilg(-\\text{sen}(x)\\bigr)=\\cfrac{10x+3}{5x^2+3x}+\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"420\" style=\"vertical-align: -14px;\"><\/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-4cdf075f9332987c97d80e87aa96be07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=24x^2-5e^{5x}-\\cfrac{8}{2\\sqrt{8x+2}}=24x^2-5e^{5x}-\\cfrac{4}{\\sqrt{8x+2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"476\" style=\"vertical-align: -16px;\"><\/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-una-resta\"><\/span> \u0625\u062b\u0628\u0627\u062a \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0637\u0631\u062d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0639\u062f \u0630\u0644\u0643 \u0633\u0646\u0628\u064a\u0646 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0637\u0631\u062d \u0627\u0644\u062f\u0648\u0627\u0644 \u0645\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0648\u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-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\"> \u0644\u0630\u0644\u0643 \u0625\u0630\u0627 \u0643\u0627\u0646 z \u0647\u0648 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \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-d195ec32e5caf166e1ae253669f8cea5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)-g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" 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-17f0dc216847872551637f676d1ff0b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{z(x+h)-z(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"215\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u0628\u062f\u0644 z \u0628\u0637\u0631\u062d \u0627\u0644\u062f\u0648\u0627\u0644 \u0641\u064a \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062d\u062f\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-40e01069bb5a50a9f8706e0b232a6c4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{\\bigl[f(x+h)-g(x+h)\\bigr]-\\bigl[f(x)-g(x)\\bigr]}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"389\" 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-0c008a2b368b6662d4184f781c60b73d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-g(x+h)-f(x)+g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"359\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0633\u0646\u0642\u0648\u0645 \u0627\u0644\u0622\u0646 \u0628\u0625\u062c\u0631\u0627\u0621 \u062a\u062d\u0648\u064a\u0644 \u0644\u0641\u0635\u0644 \u0627\u0644\u0643\u0633\u0631 \u0648\u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0637\u0631\u062d \u0643\u0633\u0631\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-e88137498b1755e2cbe6a93a99d2b769_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\left[\\frac{f(x+h)-f(x)}{h}+\\frac{-g(x+h)+g(x)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"392\" style=\"vertical-align: -16px;\"><\/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-4d2339c16c7467a19eb2387b7d84985e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\left[\\frac{f(x+h)-f(x)}{h}-\\frac{g(x+h)-g(x)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"379\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0641\u0635\u0644 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0623\u0639\u0644\u0627\u0647 \u0625\u0644\u0649 \u0646\u0647\u0627\u064a\u062a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u062a\u064a\u0646. \u0644\u0623\u0646 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0637\u0631\u062d \u062a\u0633\u0627\u0648\u064a \u0637\u0631\u062d \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-bd3b4a827d5e04a2c084d0b2cfc0a1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}-\\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"394\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 \u0646\u0638\u0631\u062a \u0639\u0646 \u0643\u062b\u0628\u060c \u0641\u0625\u0646 \u0643\u0644 \u0646\u0647\u0627\u064a\u0629 \u062a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639 \u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629\u060c \u0645\u0645\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0641\u0631\u0642 \u0645\u0633\u062a\u0648\u0641\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-5e0eb0254f80f131053caa8ee1480b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f'(x)-g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" style=\"vertical-align: -5px;\"><\/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 \u0637\u0631\u062d \u0627\u0644\u062f\u0648\u0627\u0644 (\u0627\u0644\u0635\u064a\u063a\u0629). \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0637\u0631\u062d \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627. \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0637\u0631\u062d \u0645\u0634\u062a\u0642\u0629 \u0637\u0631\u062d \u062f\u0627\u0644\u062a\u064a\u0646 \u062a\u0633\u0627\u0648\u064a \u0637\u0631\u062d \u0645\u0634\u062a\u0642\u0629 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u062d\u062f\u0629. \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u0627\u0634\u062a\u0642\u0627\u0642 \u062f\u0627\u0644\u062a\u064a\u0646 \u0645\u0646\u0641\u0635\u0644\u062a\u064a\u0646 \u062b\u0645 \u0637\u0631\u062d\u0647\u0645\u0627 \u064a\u0639\u0627\u062f\u0644 \u0637\u0631\u062d \u0627\u0644\u062f\u0627\u0644\u062a\u064a\u0646 \u0623\u0648\u0644\u064b\u0627 \u062b\u0645 \u0623\u062e\u0630 \u0627\u0644\u0645\u0634\u062a\u0642\u0629. \u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u062a\u0646\u0637\u0628\u0642 \u0646\u0641\u0633 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0644\u0649 &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%a7%d9%84%d8%b7%d8%b1%d8%ad\/\"> <span class=\"screen-reader-text\">\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0637\u0631\u062d<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f 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