{"id":394,"date":"2023-07-03T07:22:34","date_gmt":"2023-07-03T07:22:34","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d9%82%d8%a7%d8%b7%d8%b9-%d8%a7%d9%84%d8%aa%d9%85%d8%a7%d9%85\/"},"modified":"2023-07-03T07:22:34","modified_gmt":"2023-07-03T07:22:34","slug":"%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d9%82%d8%a7%d8%b7%d8%b9-%d8%a7%d9%84%d8%aa%d9%85%d8%a7%d9%85","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b4%d8%aa%d9%82-%d9%85%d9%86-%d9%82%d8%a7%d8%b7%d8%b9-%d8%a7%d9%84%d8%aa%d9%85%d8%a7%d9%85\/","title":{"rendered":"\u0645\u0634\u062a\u0642 \u0645\u0646 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645"},"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\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629 (\u0627\u0644\u0635\u064a\u063a\u0629). \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0645\u0634\u0627\u0647\u062f\u0629 \u0639\u0631\u0636 \u062a\u0648\u0636\u064a\u062d\u064a \u0644\u0635\u064a\u063a\u0629 \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. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cosecante\"><\/span> \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0643\u0648\u0632\u064a\u0643\u0627\u0646\u062a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <strong>\u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0640 x \u064a\u0633\u0627\u0648\u064a \u0646\u0627\u0642\u0635 \u062d\u0627\u0635\u0644 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0640 x \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u0645\u0631\u0628\u0639 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0640 x.<\/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-19e966c85664331b8b6c87860849678d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"416\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u064a\u0636\u064b\u0627 \u062a\u062d\u062f\u064a\u062f \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0640 x \u0645\u0637\u0631\u0648\u062d\u064b\u0627 \u0645\u0646\u0647 \u0646\u0627\u062a\u062c \u0638\u0644 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0640 x \u0641\u064a \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0640 x.<\/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-e66d4cc483a3f2c40401bf2e34fa54c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}=-\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\\cdot \\cfrac{1}{\\text{sen}(x)}=-\\text{cot}(x)\\cdot \\text{cosec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0625\u0630\u0627 \u0637\u0628\u0642\u0646\u0627 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629\u060c \u0641\u0625\u0646 <strong>\u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u062a\u0645\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629<\/strong> \u062a\u0633\u0627\u0648\u064a \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0641\u064a \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 \u0645\u0631\u0628\u0639 \u062c\u064a\u0628 \u0627\u0644\u062f\u0627\u0644\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629 \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derive-de-la-formule-cosecante.webp\" alt=\"\u0645\u0634\u062a\u0642\u0629 \u0645\u0646 \u0635\u064a\u063a\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645\" class=\"wp-image-2527\" width=\"398\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cosecante\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0623\u0646 \u0631\u0623\u064a\u0646\u0627 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645\u060c \u0633\u0646\u0642\u062f\u0645 \u0627\u0644\u0622\u0646 \u0639\u062f\u0629 \u0623\u0645\u062b\u0644\u0629. \u0644\u0630\u0644\u0643 \u064a\u0645\u0643\u0646\u0643 \u0623\u0646 \u062a\u0631\u0649 \u0628\u0627\u0644\u0636\u0628\u0637 \u0643\u064a\u0641 \u064a\u062a\u0645 \u0627\u0634\u062a\u0642\u0627\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629. <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cosecante-de-2x\"><\/span> \u0645\u062b\u0627\u0644 1: \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 2x<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u062b\u0627\u0644 \u0633\u0648\u0641 \u0646\u0631\u0649 \u0643\u0645 \u0647\u0648 \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 2x:<\/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-44aef07389e7b7d69f4ecf9e46660838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062e\u062a\u0644\u0641 \u062f\u0627\u0644\u0629 \u0648\u0633\u064a\u0637\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0639\u0646 x\u060c \u0644\u0630\u0627 \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0645\u0639 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0633\u0644\u0633\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627\u060c \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642 \u0647\u0630\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629\u060c \u0645\u0627 \u0639\u0644\u064a\u0643 \u0633\u0648\u0649 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0633\u0627\u0628\u0642\u0629: \u0641\u064a \u0648\u0633\u064a\u0637\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u0627\u0644\u062c\u064a\u0628\u060c \u0646\u0636\u0639 2x\u060c \u0648u&#8217; \u064a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639 \u0645\u0634\u062a\u0642 2x\u060c \u0623\u064a 2: <\/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-8607025c53ca3c1a2c5e05e908d61bc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2\\cdot \\text{cos}(2x)}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cosecante-de-x-al-cuadrado\"><\/span> \u0645\u062b\u0627\u0644 2: \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \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\"> \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062a\u0645\u0631\u064a\u0646\u060c \u0633\u0646\u0631\u0649 \u0645\u0642\u062f\u0627\u0631 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0640 x \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-dc9de51c8f24850940b40de616428dd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646\u0637\u0642\u064a\u064b\u0627\u060c \u064a\u062a\u0645 \u062d\u0644 \u0645\u0634\u062a\u0642\u0629 \u0647\u0630\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0634\u062a\u0642 x \u062a\u0631\u0628\u064a\u0639 \u064a\u0639\u0637\u064a 2x\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u062a\u0645\u0627\u0645 x \u0623\u0633 \u0627\u062b\u0646\u064a\u0646 \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-0a6b69e1f9851904ec2fc68bffeedc64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x\\cdot \\text{cos}(x^2)}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"454\" 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-la-cosecante-al-cubo-de-una-funcion-exponencial\"><\/span> \u0645\u062b\u0627\u0644 3: \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0627\u0644\u0645\u0643\u0639\u0628 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u064a\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-8bd5c47e8cd53ab52d3d30f55f898490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}^3(e^{5x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0647\u0645\u0627 \u0643\u0627\u0646\u062a \u0648\u0633\u064a\u0637\u0629 \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0641\u0625\u0646 \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629 \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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646 \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 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0645\u0631\u0641\u0648\u0639 \u0625\u0644\u0649 \u062b\u0644\u0627\u062b\u0629\u060c \u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u062a\u0648\u062c\u062f \u0641\u064a \u0633\u0639\u062a\u0647\u0627 \u062f\u0627\u0644\u0629 \u0623\u0633\u064a\u0629. \u0644\u0630\u0627\u060c \u0644\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627\u060c \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 \u0639\u062f\u0629 \u0645\u0631\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-9ac2ce49dfcba1b7f27696dba0a2decb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle f'(x)&amp; = 3\\text{cosec}^2(e^{5x})\\cdot\\left(-\\frac{5e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\right)\\\\[1.5ex]&amp;=-\\frac{-15\\text{cosec}^2(e^{5x})\\cdot e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"316\" 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-la-cosecante\"><\/span> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0634\u062a\u0642 \u0648\u0638\u0627\u0626\u0641 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \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-9929e2437b0ed56c3510e3e0e66745c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{cosec}(x^4-2x^2)\" 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-90abcf0539f30dc6fc72414bfc74510f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{cosec}(x^3+e^x-10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"232\" 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-86a2ea6229cced9086f8baba7afd49dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{cosec}\\bigl(\\ln(x^3+7x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" 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-45cdf124149223f4a3bec4984dc3ad3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{cosec}\\bigl(\\text{arccos}(x^7)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"217\" 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-45ae6ef998d8ab0c30309fe521b0bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{cosec}\\left(\\sqrt{9x^2-4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"226\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong> <\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1fb207498fc67f62e6c30a0baecc9549_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f('x)=-\\cfrac{(4x^3-4x)\\cdot \\text{cos}(x^4-2x^2)}{\\text{sen}^2(x^4-2x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"303\" 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-d42a3db78890f44f3cac95685ab9362e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f('x)=-\\cfrac{(3x^2+e^x)\\cdot \\text{cos}(x^3+e^x-10)}{\\text{sen}^2(x^3+e^x-10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"329\" 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-32dde68d2a11ef6a05d483b26f0a98ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp; =-\\cfrac{\\cfrac{3x^2+14x}{x^3+7x^2}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{\\cfrac{3x+14}{x^2+7x}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{(3x+14)\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{(x^2+7x)\\cdot \\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"333\" 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-b2bea25dae467cefdcc1bd48e8d9bc88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp; =-\\cfrac{-\\cfrac{7x^6}{\\sqrt{1-\\left(x^7\\right)^2}}\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =-\\cfrac{(-7x^6)\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =\\cfrac{7x^6\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"240\" width=\"348\" 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-eb70e1d7b6f2ce2636934b235904861f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\text{E) }f'(x)&amp; =-\\cfrac{\\cfrac{18x-4}{2\\cdot\\sqrt{9x^2-4x}} \\cdot \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{\\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)}\\\\[1.5ex] &amp;=-\\cfrac{(18x-4)\\cdot  \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{2\\sqrt{9x^2-4x}\\cdot \\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"165\" width=\"352\" 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-de-la-cosecante\"><\/span> \u0625\u062b\u0628\u0627\u062a \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0646\u0648\u0636\u062d \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645. \u0639\u0644\u0649 \u0639\u0643\u0633 \u0627\u0644\u0639\u0631\u0648\u0636 \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0627\u0644\u0623\u062e\u0631\u0649\u060c \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0644\u0646 \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0627\u0644\u0645\u0634\u062a\u0642\u0629\u060c \u0644\u0643\u0646\u0646\u0627 \u0633\u0646\u0628\u062f\u0623 \u0645\u0646 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062c\u0628\u0631\u064a\u064b\u0627\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0647\u064a \u0627\u0644\u0645\u0639\u0643\u0648\u0633 \u0627\u0644\u0636\u0631\u0628\u064a \u0644\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-6ac8ff987dcebfb971915b090d8dc455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x)=\\cfrac{1}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"196\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u0630\u0646 \u0623\u0646 \u0646\u0623\u062e\u0630 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0639\u062f\u0629 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\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-956e802336ed97943a839dbc059a168a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{0\\cdot \\text{sen}(x)-1\\cdot \\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"227\" 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-d26ab733704d285da0ec63f0901330b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{-\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0641\u0642\u0637 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0642\u0633\u0645\u0629 \u0646\u0635\u0644 \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645. \u0648\u0628\u0645\u0627 \u0623\u0646 \u0645\u0634\u062a\u0642\u0629 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629 \u0645\u062b\u0628\u062a\u0629 \u0628\u0627\u0644\u0641\u0639\u0644 (\u064a\u0645\u0643\u0646\u0643 \u0631\u0624\u064a\u062a\u0647\u0627 \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0637 \u0627\u0644\u062a\u0627\u0644\u064a)\u060c \u0641\u0642\u062f \u062a\u0645 \u0625\u062b\u0628\u0627\u062a \u0642\u0627\u0639\u062f\u0629 \u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0623\u064a\u0636\u064b\u0627.<\/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-\u062d\u0627\u0635\u0644-\u0627\u0644\u0642\u0633\u0645\u0629\/\">\u0625\u062b\u0628\u0627\u062a \u0645\u0634\u062a\u0642\u0629 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629<\/a><\/span><\/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\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629 (\u0627\u0644\u0635\u064a\u063a\u0629). \u0633\u062a\u062c\u062f \u0623\u064a\u0636\u064b\u0627 \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0645\u0634\u062a\u0642\u0629 \u0642\u0627\u0637\u0639 \u0627\u0644\u062a\u0645\u0627\u0645. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c 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