{"id":385,"date":"2023-07-03T03:43:52","date_gmt":"2023-07-03T03:43:52","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e6%ad%a3%e5%89%b2%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-07-03T03:43:52","modified_gmt":"2023-07-03T03:43:52","slug":"%e5%8f%8c%e6%9b%b2%e6%ad%a3%e5%89%b2%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e6%ad%a3%e5%89%b2%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u53cc\u66f2\u6b63\u5272\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cc\u66f2\u6b63\u5272\u3002\u60a8\u5c06\u627e\u5230\u53cc\u66f2\u6b63\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u4ee5\u53ca\u6b64\u7c7b\u5bfc\u6570\u7684\u51e0\u4e2a\u5de5\u4f5c\u793a\u4f8b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-secante-hiperbolica\"><\/span>\u53cc\u66f2\u6b63\u5272\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u7684\u53cc\u66f2\u6b63\u5272\u7684\u5bfc\u6570\u7b49\u4e8e\u51cf\u53bb x \u7684\u53cc\u66f2\u6b63\u5272\u4e58\u4ee5 x \u7684\u53cc\u66f2\u6b63\u5207\u7684\u4e58\u79ef\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-c07ba93179ede436aa585653d7c4e07f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sech}(x)\\cdot \\text{tanh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"476\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u51fd\u6570\u7684\u53cc\u66f2\u6b63\u5272\u7684\u5bfc\u6570<\/strong>\u51cf\u53bb\u51fd\u6570\u7684\u53cc\u66f2\u6b63\u5272\u4e58\u4ee5\u51fd\u6570\u7684\u53cc\u66f2\u6b63\u5207\u4e58\u4ee5\u6240\u8ff0\u51fd\u6570\u7684\u5bfc\u6570\u7684\u4e58\u79ef\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-f51426f6d6f9cb5df2135bf16c720ce1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sech}(u)\\cdot \\text{tanh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"504\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u53cc\u66f2\u6b63\u5272\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\u4e3a\uff1a <\/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-secante-hyperbolique.webp\" alt=\"\u7531\u53cc\u66f2\u6b63\u5272\u5bfc\u51fa\" class=\"wp-image-2756\" width=\"473\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u8bf7\u6ce8\u610f\uff0c\u4e24\u4e2a\u8868\u8fbe\u5f0f\u5b9e\u9645\u4e0a\u5c5e\u4e8e\u4e00\u4e2a\u516c\u5f0f\u3002\u552f\u4e00\u7684\u533a\u522b\u662f\u5728\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4e2d\u5e94\u7528\u4e86\u94fe\u5f0f\u6cd5\u5219\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-secante-hiperbolica\"><\/span>\u53cc\u66f2\u6b63\u5272\u7684\u5bfc\u6570\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u53cc\u66f2\u6b63\u5272\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u5c06\u770b\u5230\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u51e0\u4e2a\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b1<\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1077c4d8341190071e3d52fc9b7dd587_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5728\u53cc\u66f2\u6b63\u5272\u53c2\u6570\u4e2d\u5177\u6709\u4e0e x \u4e0d\u540c\u7684\u51fd\u6570\uff0c\u56e0\u6b64\u8981\u5bfc\u51fa\u5b83\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u516c\u5f0f\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-f51426f6d6f9cb5df2135bf16c720ce1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sech}(u)\\cdot \\text{tanh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"504\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e\u51fd\u6570 2x \u662f\u7ebf\u6027\u7684\uff0c\u56e0\u6b64\u5b83\u7684\u5bfc\u6570\u4e3a 2\u3002\u56e0\u6b64\uff0c\u8981\u6c42\u5bfc\u6570\uff0c\u6211\u4eec\u53ea\u9700\u5c06\u516c\u5f0f\u4e2d\u7684 u \u66ff\u6362\u4e3a 2x\uff0c\u5c06 u&#8217; \u66ff\u6362\u4e3a 2\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-947df587e6457c9a82023c6ea76e3d1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sech}(2x)\\cdot \\text{tanh}(2x)\\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"525\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b2<\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f759fd3a41187cc0764c458c21481eb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8fd9\u4e2a\u7ec3\u4e60\u7684\u529f\u80fd\u662f\u590d\u5408\u7684\uff0c\u56e0\u4e3a\u53cc\u66f2\u6b63\u5272\u5728\u5176\u8bba\u8bc1\u4e2d\u8fd8\u6709\u53e6\u4e00\u4e2a\u529f\u80fd\u3002\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u53cc\u66f2\u6b63\u5272\u516c\u5f0f\u548c\u94fe\u5f0f\u6cd5\u5219\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-f51426f6d6f9cb5df2135bf16c720ce1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sech}(u)\\cdot \\text{tanh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"504\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> x \u7684\u5bfc\u6570\u5347\u5230 2 \u5f97\u5230 2x\uff0c\u56e0\u6b64 x \u5e73\u65b9\u7684\u53cc\u66f2\u6b63\u5272\u7684\u5bfc\u6570\u4e3a\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-2afe9c3dc5fc592bf5714f34f8016ef8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sech}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sech}(x^2)\\cdot \\text{tanh}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"532\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cc\u66f2\u6b63\u5272\u3002\u60a8\u5c06\u627e\u5230\u53cc\u66f2\u6b63\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u4ee5\u53ca\u6b64\u7c7b\u5bfc\u6570\u7684\u51e0\u4e2a\u5de5\u4f5c\u793a\u4f8b\u3002 \u53cc\u66f2\u6b63\u5272\u7684 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e6%ad%a3%e5%89%b2%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u53cc\u66f2\u6b63\u5272\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-385","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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