{"id":389,"date":"2023-07-03T01:50:55","date_gmt":"2023-07-03T01:50:55","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%b9%b3%e8%83%b6%e8%a1%8d%e7%94%9f%e7%89%a9\/"},"modified":"2023-07-03T01:50:55","modified_gmt":"2023-07-03T01:50:55","slug":"%e5%8f%8c%e6%9b%b2%e4%b9%b3%e8%83%b6%e8%a1%8d%e7%94%9f%e7%89%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%b9%b3%e8%83%b6%e8%a1%8d%e7%94%9f%e7%89%a9\/","title":{"rendered":"\u53cc\u66f2\u4f59\u5272\u5f27\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cc\u66f2\u53cd\u4f59\u5272\u3002\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u53cc\u66f2\u53cd\u4f59\u5272\u5bfc\u6570\u7684\u5de5\u4f5c\u793a\u4f8b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-arcocosecante-hiperbolica\"><\/span>\u53cc\u66f2\u4f59\u5272\u5f27\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u7684\u53cd\u53cc\u66f2\u4f59\u5272\u7684\u5bfc\u6570\u7b49\u4e8e\u8d1f 1 \u9664\u4ee5 x \u4e58\u4ee5\u4e00\u52a0 x \u5e73\u65b9\u6839\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-0367e01bffbaea95b002c0261e6597d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccsch}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-1}{x\\sqrt{1+x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u51fd\u6570\u7684\u53cd\u53cc\u66f2\u4f59\u5272\u7684\u5bfc\u6570<\/strong>\u662f\u51cf\u53bb\u8be5\u51fd\u6570\u7684\u5bfc\u6570\u9664\u4ee5\u8be5\u51fd\u6570\u4e58\u4ee5\u4e00\u7684\u6839\u52a0\u4e0a\u51fd\u6570\u5e73\u65b9\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-c84a1cfa851e7f8db30d3953efcf1b2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccsch}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-u'}{u\\sqrt{1+u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u53cc\u66f2\u53cd\u4f59\u5272\u51fd\u6570\u5bfc\u6570\u7684\u8ba1\u7b97\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-larccosecante-hyperbolique.webp\" alt=\"\u53cc\u66f2\u4f59\u5272\u5f27\u7684\u5bfc\u6570\" class=\"wp-image-2797\" width=\"365\" height=\"266\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u867d\u7136\u6211\u4eec\u63d0\u51fa\u4e86\u4e24\u4e2a\u516c\u5f0f\uff0c\u4f46\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u5b83\u4eec\u662f\u4e0d\u540c\u7684\u3002\u5982\u679c\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4e0e\u7b2c\u4e00\u4e2a\u516c\u5f0f\u7c7b\u4f3c\uff0c\u4f46\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-arcocosecante-hiperbolica\"><\/span>\u53cc\u66f2\u4f59\u5272\u5f27\u7684\u5bfc\u6570\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u53cc\u66f2\u53cd\u6b63\u4f59\u5272\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u5c06\u5bfc\u51fa\u4e24\u4e2a\u8fd9\u6837\u7684\u51fd\u6570\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\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-24a3e6958bf4fd28f73062bb78280dc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccsch}(3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u672c\u7ec3\u4e60\u4e2d\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u53cd\u53cc\u66f2\u4f59\u5272\u7684\u5bfc\u6570\u516c\u5f0f\uff0c\u56e0\u4e3a\u5728\u53c2\u6570\u4e2d\u5b58\u5728\u4e00\u4e2a\u4e0e x \u4e0d\u540c\u7684\u51fd\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-c84a1cfa851e7f8db30d3953efcf1b2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccsch}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-u'}{u\\sqrt{1+u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u6c42\u5bfc\u6570\uff0c\u6211\u4eec\u9700\u8981\u5c06 u \u66ff\u6362\u4e3a 3x\uff0c\u5c06 u&#8217; \u66ff\u6362\u4e3a\u5176\u5bfc\u6570\uff0c\u5373 3\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-aa1b0c4d4233e274d3996620bacdb869_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccsch}(3x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-3}{3x\\sqrt{1+(3x)^2}}=\\cfrac{-3}{3x\\sqrt{1+9x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"582\" style=\"vertical-align: -16px;\"><\/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-a99a903e923a1fd4dc9442e903f244ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccsch}(x^5-2x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u7684\u53cc\u66f2\u53cd\u4f59\u5272\u53c2\u6570\u4e2d\u6709\u4e00\u4e2a\u591a\u9879\u5f0f\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u8fd8\u9700\u8981\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u63a8\u5bfc\u5b83\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-c84a1cfa851e7f8db30d3953efcf1b2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccsch}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{-u'}{u\\sqrt{1+u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"435\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u53c2\u6570\u51fd\u6570\u7684\u5bfc\u6570\u653e\u5165\u5206\u6570\u7684\u5206\u5b50\u4e2d\uff0c\u5e76\u5728\u5206\u6bcd\u4e2d\u901a\u8fc7\u591a\u9879\u5f0f\u51fd\u6570\u6539\u53d8 u\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-6257584425bd348ba75c7680d8ff6f70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f(x)=\\text{arccsch}(x^5-2x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}f'(x)&amp;=\\cfrac{-(5x^4-6x^2)}{(x^5-2x^3)\\sqrt{1+(x^5-2x^3)^2}}\\\\[1.5ex] &amp;=\\cfrac{-5x^4+6x^2}{(x^5-2x^3)\\sqrt{1+(x^5-2x^3)^2}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"117\" width=\"634\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"articulos-relacionados\"><\/span>\u7c7b\u4f3c\u5546\u54c1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u53cc\u66f2\u53cd\u4f59\u5f26\u5bfc\u6570\/\">\u53cc\u66f2\u53cd\u4f59\u5f26\u7684\u5bfc\u6570<\/a><\/span><\/li>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u53cc\u66f2\u4f59\u5272\u7684\u5bfc\u6570\/\">\u53cc\u66f2\u4f59\u5272\u7684\u5bfc\u6570<\/a><\/span><\/li>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u53cc\u66f2\u4f59\u5f26\u5bfc\u6570\/\">\u53cc\u66f2\u4f59\u5f26\u7684\u5bfc\u6570<\/a><\/span><\/li>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u53cd\u4f59\u5272\u5bfc\u6570\/\">\u4f59\u5272\u5f27\u7684\u5bfc\u6570<\/a><\/span><\/li>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u7531\u4f59\u5272\u5bfc\u51fa\/\">\u7531\u4f59\u5272\u5bfc\u51fa<\/a><\/span><\/li>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u62c9\u8003\u8f9b\u884d\u751f\u7269\/\">\u53cd\u4f59\u5f26\u7684\u5bfc\u6570<\/a><\/span><\/li>\n<li><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u7531\u4f59\u5f26\u5bfc\u51fa\/\">\u4f59\u5f26\u7684\u5bfc\u6570<\/a><\/span><\/li>\n<\/ul>\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\u53cd\u4f59\u5272\u3002\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u53cc\u66f2\u53cd\u4f59\u5272\u5bfc\u6570\u7684\u5de5\u4f5c\u793a\u4f8b\u3002 \u53cc\u66f2\u4f59\u5272\u5f27\u7684\u5bfc\u6570\u516c\u5f0f x &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%8f%8c%e6%9b%b2%e4%b9%b3%e8%83%b6%e8%a1%8d%e7%94%9f%e7%89%a9\/\"> <span class=\"screen-reader-text\">\u53cc\u66f2\u4f59\u5272\u5f27\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-389","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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