{"id":376,"date":"2023-07-03T14:10:00","date_gmt":"2023-07-03T14:10:00","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%bd%99%e5%bc%a6%e5%af%bc%e6%95%b0\/"},"modified":"2023-07-03T14:10:00","modified_gmt":"2023-07-03T14:10:00","slug":"%e5%8f%8c%e6%9b%b2%e4%bd%99%e5%bc%a6%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%bc%a6%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u53cc\u66f2\u4f59\u5f26\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cc\u66f2\u4f59\u5f26\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u4f1a\u627e\u5230\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u6700\u540e\uff0c\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-coseno-hiperbolico\"><\/span>\u53cc\u66f2\u4f59\u5f26\u63a8\u5bfc\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u7684\u53cc\u66f2\u4f59\u5f26\u7684\u5bfc\u6570\u662f x \u7684\u53cc\u66f2\u6b63\u5f26\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-2c3935efe4db8dd3b7852cc93509c06c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"394\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u51fd\u6570\u7684\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570<\/strong>\u7b49\u4e8e\u8be5\u51fd\u6570\u7684\u53cc\u66f2\u6b63\u5f26\u4e0e\u8be5\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-764d8e891bc33a54d2ad73393df144c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4e0e\u7b2c\u4e00\u4e2a\u516c\u5f0f\u76f8\u540c\uff0c\u552f\u4e00\u7684\u533a\u522b\u662f\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u5e94\u7528\u4e86\u94fe\u5f0f\u6cd5\u5219\u3002\u6240\u4ee5\uff0c\u7b2c\u4e00\u4e2a\u516c\u5f0f\u53ea\u80fd\u7528\u6765\u63a8\u5bfcx\u7684\u53cc\u66f2\u4f59\u5f26\uff0c\u800c\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u53ef\u4ee5\u7528\u6765\u63a8\u5bfc\u4efb\u4f55\u7c7b\u578b\u51fd\u6570\u7684\u53cc\u66f2\u4f59\u5f26\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-du-cosinus-hyperbolique.webp\" alt=\"\" class=\"wp-image-2064\" width=\"427\" height=\"278\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\u4e0e\u4f59\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\u4e0d\u540c\uff0c\u5c3d\u7ba1\u5b83\u4eec\u6709\u4e00\u4e9b\u76f8\u4f3c\u4e4b\u5904\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u89c1\uff1a<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u7531\u4f59\u5f26\u5bfc\u51fa\/\">\u4f59\u5f26\u5bfc\u6570\u516c\u5f0f<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-coseno-hiperbolico\"><\/span>\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u6c42\u89e3\u4e0b\u9762\u6b64\u7c7b\u4e09\u89d2\u51fd\u6570\u7684\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\u3002\u8bf7\u8bb0\u4f4f\uff0c\u60a8\u53ef\u4ee5\u5728\u8bc4\u8bba\u4e2d\u63d0\u51fa\u4efb\u4f55\u95ee\u9898\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-coseno-hiperbolico-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \u53cc\u66f2\u4f59\u5f26\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/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-6c79bebc7f8b263bee01848f5babea49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u53cc\u66f2\u4f59\u5f26\u7684\u53c2\u6570\u4e2d\u6709\u4e00\u4e2a\u4e0e x \u4e0d\u540c\u7684\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bf9\u53cc\u66f2\u4f59\u5f26\u6c42\u5bfc\u7684\u516c\u5f0f\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-764d8e891bc33a54d2ad73393df144c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 2x \u7684\u5bfc\u6570\u662f 2\uff0c\u56e0\u6b64 2x \u7684\u53cc\u66f2\u4f59\u5f26\u7684\u5bfc\u6570\u662f 2x \u4e58\u4ee5 2 \u7684\u53cc\u66f2\u6b63\u5f26\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-b84c1d5aa09cb545408a723b54f8fbf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(2x)\\cdot 2=2\\text{cosh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"533\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-coseno-hiperbolico-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\u7684\u53cc\u66f2\u4f59\u5f26\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/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-daf8b19f319b047a8b677ff1f158cd16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"122\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u9762\u770b\u5230\u7684\uff0c\u53cc\u66f2\u4f59\u5f26\u51fd\u6570\u7684\u5bfc\u6570\u89c4\u5219\u662f\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-764d8e891bc33a54d2ad73393df144c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u4e00\u65b9\u9762\u63a8\u5bfc\u51fa\u4e8c\u6b21\u51fd\u6570 x <sup>2<\/sup> \uff0c\u5b83\u7ed9\u51fa 2x\uff0c\u7136\u540e\u6211\u4eec\u8ba1\u7b97\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\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-3f15e7e138793e4cdcb3da8a84724d5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"443\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-del-coseno-hiperbolico\"><\/span>\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\u516c\u5f0f\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u4ece\u53cc\u66f2\u4f59\u5f26\u5bfc\u51fa\u7684\u516c\u5f0f\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5b83\u7684\u6765\u6e90\u3002\u5982\u679c\u6211\u4eec\u4ece\u53cc\u66f2\u4f59\u5f26\u7684\u8868\u8fbe\u5f0f\u5f00\u59cb\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-441432af7fa8c1db95476b9541e222d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x)=\\cfrac{e^x+e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u4ece\u8868\u8fbe\u5f0f\u4e24\u8fb9\u63a8\u5bfc\u51fa\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-5ace35f9bdf59afdfd1dc06cccade202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bigl(\\text{cosh}(x)\\bigr)'=\\left(\\frac{e^x+e^{-x}}{2}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"200\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u53f3\u8fb9\u6709\u9664\u6cd5\uff0c\u6240\u4ee5\u6211\u4eec\u5e94\u7528\u5546\u7684\u5bfc\u6570\u516c\u5f0f\u6765\u6c42\u5bfc\u6570\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-dacf4babd2368ad5d84913142cd1c988_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}'(x)=\\frac{(e^x-e^{-x})\\cdot 2}{2^2}=\\frac{e^x-e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u9664\u5546\u7684\u5bfc\u6570\/\">\u4ece\u5546\u5bfc\u51fa\u7684\u89c4\u5219<\/a><\/span><\/p>\n<p>\u5982\u679c\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u5f97\u5230\u7684\u8868\u8fbe\u5f0f\u4e0e\u53cc\u66f2\u6b63\u5f26\u7684\u8868\u8fbe\u5f0f\u76f8\u5bf9\u5e94\uff0c\u8fd9\u610f\u5473\u7740\u4ee5\u4e0b\u7b49\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-9fafe72628e85aed5276d0a6b9104baa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}'(x)=\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"143\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u5f97\u51fa\u4e86\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\u7684\u89c4\u5219\uff0c\u5e76\u4e14\u5b83\u5df2\u7ecf\u88ab\u8bc1\u660e\u4e86\u3002<\/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\u4f59\u5f26\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u4f1a\u627e\u5230\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u6700\u540e\uff0c\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u6b64\u7c7b\u4e09\u89d2\u5bfc &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%bd%99%e5%bc%a6%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u53cc\u66f2\u4f59\u5f26\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-376","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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