{"id":375,"date":"2023-07-03T15:44:25","date_gmt":"2023-07-03T15:44:25","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e6%ad%a3%e5%bc%a6%e5%af%bc%e6%95%b0\/"},"modified":"2023-07-03T15:44:25","modified_gmt":"2023-07-03T15:44:25","slug":"%e5%8f%8c%e6%9b%b2%e6%ad%a3%e5%bc%a6%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%bc%a6%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u53cc\u66f2\u6b63\u5f26\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u53cc\u66f2\u6b63\u5f26\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u770b\u5230\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u7684\u51e0\u4e2a\u5df2\u6c42\u89e3\u793a\u4f8b\u3002\u6700\u540e\uff0c\u6211\u4eec\u8bc1\u660e\u4e86\u6b64\u7c7b\u4e09\u89d2\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-del-seno-hiperbolico\"><\/span>\u53cc\u66f2\u6b63\u5f26\u63a8\u5bfc\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u7684\u53cc\u66f2\u6b63\u5f26\u7684\u5bfc\u6570\u662f x \u7684\u53cc\u66f2\u4f59\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-5824c2bfe983f8a9b725fab69a97ecca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(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\u6b63\u5f26\u5bfc\u6570<\/strong>\u7b49\u4e8e\u8be5\u51fd\u6570\u7684\u53cc\u66f2\u4f59\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-8d49318fdfae22c716e856e18e7440db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5b9e\u9645\u4e0a\uff0c\u4e0a\u9762\u4e24\u4e2a\u516c\u5f0f\u662f\u76f8\u540c\u7684\uff0c\u552f\u4e00\u7684\u533a\u522b\u662f\u5728\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4e2d\u6211\u4eec\u5e94\u7528\u4e86\u94fe\u5f0f\u6cd5\u5219\u3002\u7531\u4e8e x \u7684\u5bfc\u6570\u4e3a 1\uff0c\u56e0\u6b64\u8fd9\u4e0d\u4f1a\u6539\u53d8\u51fd\u6570\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-sinus-hyperbolique.webp\" alt=\"\u53cc\u66f2\u6b63\u5f26\u7684\u5bfc\u6570\" class=\"wp-image-2021\" width=\"423\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\u4e0e<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6b63\u5f26\u5bfc\u6570\/\">\u6b63\u5f26\u5bfc\u6570\u7684\u516c\u5f0f<\/a><\/span>\u975e\u5e38\u76f8\u4f3c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-seno-hiperbolico\"><\/span>\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u73b0\u5728\u5c31\u7ee7\u7eed\u6c42\u89e3\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u7684\u51e0\u4e2a\u4f8b\u5b50\u3002\u56e0\u6b64\uff0c\u60a8\u80af\u5b9a\u5bf9\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\u6ca1\u6709\u7591\u95ee\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-seno-hiperbolico-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \u53cc\u66f2\u6b63\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-11e5d630f508c66d1be884d9a6454d30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5728\u53cc\u66f2\u6b63\u5f26\u53c2\u6570\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u4e0e x \u4e0d\u540c\u7684\u51fd\u6570\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u516c\u5f0f\u548c\u94fe\u5f0f\u6cd5\u5219\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-8d49318fdfae22c716e856e18e7440db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(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\u4e3a 2\uff0c\u56e0\u6b64 2x \u7684\u53cc\u66f2\u6b63\u5f26\u7684\u5bfc\u6570\u5c06\u662f 2x \u4e58\u4ee5 2 \u7684\u53cc\u66f2\u4f59\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-4e763d6973e52217ac14f6f6b3344737_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(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-seno-hiperbolico-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\u7684\u53cc\u66f2\u6b63\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-432b20159f3f131533249e4ee44702e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u53cc\u66f2\u6b63\u5f26\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\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-8d49318fdfae22c716e856e18e7440db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u4e8c\u6b21\u51fd\u6570x <sup>2<\/sup>\u7684\u5bfc\u6570\u662f2x\u3002\u56e0\u6b64\u6574\u4e2a\u51fd\u6570\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-56db45ee5a51f7ed624f7e88ce4cf906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cosh}(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-seno-hiperbolico\"><\/span>\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u516c\u5f0f\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u6f14\u793a\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4ece\u53cc\u66f2\u6b63\u5f26\u7684\u6570\u5b66\u5b9a\u4e49\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-ef003e8f8367d5cacacb4d67fb8dbd01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(x)=\\cfrac{e^x-e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u63a8\u5bfc\u51fa\u7b49\u5f0f\u7684\u4e24\u8fb9\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-39aa6ef096997dc19e3850036a95b0d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bigl(\\text{senh}(x)\\bigr)'=\\left(\\frac{e^x-e^{-x}}{2}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"201\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u5bfc\u51fa\u65b9\u7a0b\u7684\u53f3\u4fa7\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u9664\u6cd5\u5bfc\u6570\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-c11def15692e1374b5f75743bfc04b40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}'(x)=\\frac{(e^x+e^{-x})\\cdot 2}{2^2}=\\frac{e^x+e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"284\" 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\/\u6307\u6570\u51fd\u6570\u7684\u5bfc\u6570\/\">\u4ee5 e \u4e3a\u5e95\u7684\u6307\u6570\u51fd\u6570\u7684\u5bfc\u6570<\/a><\/span><\/p>\n<p>\u51c6\u786e\u5730\u8bf4\uff0c\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86\u5b9a\u4e49\u53cc\u66f2\u4f59\u5f26\u7684\u8868\u8fbe\u5f0f\u3002\u4ece\u800c\u8bc1\u660e\u53cc\u66f2\u6b63\u5f26\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-fb3756efaf241b9435c36856a5dad2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}'(x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"143\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u53cc\u66f2\u6b63\u5f26\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u770b\u5230\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u7684\u51e0\u4e2a\u5df2\u6c42\u89e3\u793a\u4f8b\u3002\u6700\u540e\uff0c\u6211\u4eec\u8bc1\u660e\u4e86\u6b64\u7c7b\u4e09\u89d2 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e6%ad%a3%e5%bc%a6%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u53cc\u66f2\u6b63\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-375","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u53cc\u66f2\u6b63\u5f26\u7684\u5bfc\u6570 - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/cn\/\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u53cc\u66f2\u6b63\u5f26\u7684\u5bfc\u6570 - Mathority\" \/>\n<meta property=\"og:description\" content=\"\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u53cc\u66f2\u6b63\u5f26\uff08\u516c\u5f0f\uff09\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u770b\u5230\u53cc\u66f2\u6b63\u5f26\u5bfc\u6570\u7684\u51e0\u4e2a\u5df2\u6c42\u89e3\u793a\u4f8b\u3002\u6700\u540e\uff0c\u6211\u4eec\u8bc1\u660e\u4e86\u6b64\u7c7b\u4e09\u89d2 &hellip; 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