{"id":387,"date":"2023-07-03T02:36:56","date_gmt":"2023-07-03T02:36:56","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%bd%99%e5%88%87%e5%80%bc%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-07-03T02:36:56","modified_gmt":"2023-07-03T02:36:56","slug":"%e5%8f%8c%e6%9b%b2%e4%bd%99%e5%88%87%e5%80%bc%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%bd%99%e5%88%87%e5%80%bc%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cc\u66f2\u4f59\u5207\u503c\u3002\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u53cc\u66f2\u4f59\u5207\u503c\u5bfc\u6570\u7684\u793a\u4f8b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cotangente-hiperbolica\"><\/span>\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u7684\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570\u7b49\u4e8e\u51cf\u53bb x \u7684\u5e73\u65b9\u7684\u53cc\u66f2\u4f59\u5272\u503c\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-159a0cc5b4ec54f5e5180986bf97e326_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(x)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"439\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u51fd\u6570\u53cc\u66f2\u4f59\u5207\u7684\u5bfc\u6570<\/strong>\u51cf\u53bb\u51fd\u6570\u7684\u53cc\u66f2\u4f59\u5272\u4e58\u4ee5\u8be5\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce8d53b14c0a0283174650861f34526b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u5728\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4e2d\u5e94\u7528\u4e86\u94fe\u5f0f\u6cd5\u5219\uff0c\u5e76\u4e14\u5f53\u53cc\u66f2\u4f59\u5207\u53c2\u6570\u4e2d\u5b58\u5728 x \u4ee5\u5916\u7684\u51fd\u6570\u65f6\uff0c\u5c06\u4f7f\u7528\u8be5\u516c\u5f0f\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-de-la-cotangente-hyperbolique.webp\" alt=\"\u7531\u53cc\u66f2\u4f59\u5207\u5bfc\u51fa\" class=\"wp-image-2771\" width=\"456\" height=\"287\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u60a8\u53ef\u80fd\u4f1a\u5728\u4e00\u4e9b\u6570\u5b66\u4e66\u7c4d\u4e2d\u53d1\u73b0\u4f59\u5207\u7684\u5bfc\u6570\u662f\u53e6\u4e00\u4e2a\uff0c\u56e0\u4e3a\u4ee5\u4e0b\u4e09\u4e2a\u8868\u8fbe\u5f0f\u662f\u7b49\u6548\u7684\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f9bb22138450fbc59797ea330d247b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\text{cosech}^2(x)=1-\\text{cotgh}^2(x)=-\\cfrac{1}{\\text{senh}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"391\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p>\u663e\u7136\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e09\u4e2a\u8868\u8fbe\u5f0f\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u6765\u5bfc\u51fa\u53cc\u66f2\u4f59\u5207\u503c\uff0c\u4f46\u6700\u5e38\u7528\u7684\u662f\u53cc\u66f2\u4f59\u5272\u5e73\u65b9\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cotangente-hiperbolica\"><\/span>\u53cc\u66f2\u4f59\u5207\u5bfc\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u4e86\u51fd\u6570\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u6c42\u89e3\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u51e0\u4e2a\u4f8b\u5b50\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b1<\/h3>\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5c06\u770b\u5230\u51fd\u6570 2x \u7684\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c7d3005851f13f7f239dbd5f976d87b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"132\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u53cc\u66f2\u4f59\u5207\u53c2\u6570\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a x \u4ee5\u5916\u7684\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u4f7f\u7528\u5e26\u6709\u94fe\u5f0f\u6cd5\u5219\u7684\u516c\u5f0f\u6765\u8fdb\u884c\u63a8\u5bfc\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce8d53b14c0a0283174650861f34526b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e 2x \u662f\u4e00\u6b21\u9879\uff0c\u5176\u5bfc\u6570\u4e3a 2\u3002\u56e0\u6b64\uff0c\u8981\u6c42 2x \u53cc\u66f2\u4f59\u5207\u7684\u5bfc\u6570\uff0c\u6211\u4eec\u53ea\u9700\u5c06 2x \u653e\u5165\u53cc\u66f2\u4f59\u5272\u7684\u5e73\u65b9\u53c2\u6570\u4e2d\uff0c\u7136\u540e\u4e58\u4ee5 2\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9805919c1591f35bad147992046725c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(2x)\\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"478\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b2<\/h3>\n<p>\u5728\u7b2c\u4e8c\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u786e\u5b9a\u591a\u9879\u5f0f\u51fd\u6570\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570\u503c\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a861bc1c6734dac702da19a7f9614eb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(3x^4-5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u9762\u770b\u5230\u7684\uff0c\u5bfc\u51fa\u51fd\u6570\u53cc\u66f2\u4f59\u5207\u7684\u89c4\u5219\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce8d53b14c0a0283174650861f34526b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u672c\u7ec3\u4e60\u7684\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d9b5b922da23b4196f7ee1edd440f72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotgh}(3x^4-5x)\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=-\\text{cosech}^2(3x^4-5x)\\cdot(12x^3-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"582\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cc\u66f2\u4f59\u5207\u503c\u3002\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u53cc\u66f2\u4f59\u5207\u503c\u5bfc\u6570\u7684\u793a\u4f8b\u3002 \u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570\u516c\u5f0f x \u7684\u53cc\u66f2 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%bd%99%e5%88%87%e5%80%bc%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u53cc\u66f2\u4f59\u5207\u503c\u7684\u5bfc\u6570<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[6],"tags":[],"class_list":["post-387","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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