{"id":47,"date":"2023-09-17T10:54:18","date_gmt":"2023-09-17T10:54:18","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%bd%99%e5%88%87%e5%80%bc%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-09-17T10:54:18","modified_gmt":"2023-09-17T10:54:18","slug":"%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\/%e4%bd%99%e5%88%87%e5%80%bc%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u4f59\u5207\u503c\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u4f59\u5207\u503c\u3002\u60a8\u4f1a\u627e\u5230\u4f59\u5207\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u751a\u81f3\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u6211\u4eec\u8bc1\u660e\u4e86\u4f59\u5207\u5bfc\u6570\u7684\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cotangente\"><\/span>\u4f59\u5207\u503c\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u4f59\u5207\u7684\u5bfc\u6570\u7b49\u4e8e x \u6b63\u5f26\u5e73\u65b9\u7684\u8d1f\u4e00\u3002<\/strong> x \u4f59\u5207\u503c\u7684\u5bfc\u6570\u4e5f\u7b49\u4e8e\u51cf\u53bb x \u4f59\u5272\u503c\u7684\u5e73\u65b9\uff0c\u518d\u51cf\u53bb 1 \u52a0 x \u4f59\u5207\u503c\u5e73\u65b9\u7684\u548c\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-0a3653f5c765d773ebc789107bf1a825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cotg}(x)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=-\\cfrac{1}{\\text{sen}^2(x)}=-\\text{cosec}^2(x)=-\\left(1+\\text{cotg}^2(x)\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"393\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u53c2\u6570\u4f59\u5207\u662f x \u4ee5\u5916\u7684\u51fd\u6570\uff0c\u5219\u51fd\u6570\u4f59\u5207\u7684\u5bfc\u6570\u516c\u5f0f\u4e0e\u524d\u9762\u7684\u76f8\u540c\uff0c\u4f46\u5c06\u8868\u8fbe\u5f0f\u4e58\u4ee5\u53c2\u6570\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-38ea1d1edeaf5664c56a946b5a87577d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cotg}(u)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}=-u' \\cdot \\text{cosec}^2(u)=-u' \\cdot \\left(1+\\text{cotg}^2(u)\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"445\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u8fd9\u610f\u5473\u7740\u5b58\u5728\u4e09\u4e2a\u4e0d\u540c\u7684\u516c\u5f0f\u6765\u6c42\u4f59\u5207\u7684\u5bfc\u6570\u3002\u4f46\u662f\uff0c\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u6ca1\u6709\u5fc5\u8981\u4f7f\u7528\u6240\u6709\u4e09\u4e2a\u516c\u5f0f\uff0c\u4f46\u60a8\u53ef\u4ee5\u4f7f\u7528\u60a8\u559c\u6b22\u7684\u516c\u5f0f\u6765\u63a8\u5bfc\u5b83\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.webp\" alt=\"\u7531\u4f59\u5207\u5bfc\u51fa\" class=\"wp-image-2685\" width=\"428\" height=\"361\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cotangente\"><\/span>\u4f59\u5207\u5bfc\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u51fd\u6570\u4f59\u5207\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u5728\u672c\u8282\u4e2d\u6211\u4eec\u5c06\u6c42\u89e3\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cotangente-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \u4f59\u5207\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5c06\u770b\u5230\u51fd\u6570 2x \u7684\u4f59\u5207\u503c\u7684\u5bfc\u6570\u662f\u591a\u5c11\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-b95db136ea1e222c9f810d724216b083_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u6240\u770b\u5230\u7684\uff0c\u8981\u8ba1\u7b97\u4f59\u5207\u7684\u5bfc\u6570\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u770b\u5230\u7684\u4e09\u4e2a\u516c\u5f0f\u4e4b\u4e00\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u6b63\u5f26\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-b071b560415fc193171a74fd0b4b84cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"409\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e 2x \u662f\u4e00\u6b21\u9879\uff0c\u56e0\u6b64\u5176\u5bfc\u6570\u4e3a 2\u3002\u56e0\u6b64 2x \u7684\u4f59\u5207\u503c\u7684\u5bfc\u6570\u4e3a\u8d1f\u4e8c\u9664\u4ee5 2x \u7684\u6b63\u5f26\u5e73\u65b9\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-4151decbf7dd792fd0ea6aa6ca4b55f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"426\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cotangente-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\u4f59\u5207\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u7b2c\u4e8c\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u786e\u5b9a x \u5e73\u65b9\u7684\u4f59\u5207\u503c\u7684\u5bfc\u6570\u662f\u591a\u5c11\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-ec3733080f720a5115d2d6719d33d7e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u4f59\u5207\u53c2\u6570\u7684\u51fd\u6570\u4e0d\u662f x\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u5fae\u5206\u4f59\u5207\u3002<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-b071b560415fc193171a74fd0b4b84cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"409\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> x \u5e73\u65b9\u7684\u5bfc\u6570\u4e3a 2x\uff0c\u56e0\u6b64 x <sup>2<\/sup>\u4f59\u5207\u7684\u5bfc\u6570\u4e3a\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><meta charset=\"utf-8\"><\/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-6aef87160d0da1da0b32e1e200f31b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}(x^2)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"424\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-cotangente-al-cubo\"><\/span>\u793a\u4f8b 3\uff1a\u4f59\u5207\u4e09\u6b21\u65b9\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u6c42\u51fa\u591a\u9879\u5f0f\u51fd\u6570\u7684\u4e09\u6b21\u4f59\u5207\u503c\u7684\u5bfc\u6570\u662f\u591a\u5c11\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-9be8c3c10c50e3ef6bb701a11d3f46c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cotg}^3(x^5-6x^2+10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"217\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u51fd\u6570\u7ec4\u5408\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u548c\u5e42\u5bfc\u6570\u516c\u5f0f\u6765\u6c42\u4f59\u5207\u7684\u5bfc\u6570\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><meta charset=\"utf-8\"><\/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-ed0c6f314584b0f00021e3833de2b223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=-3\\cdot\\text{cotg}^2(x^5-6x^2+10)\\cdot\\frac{5x^4-12x}{\\text{sen}^2(x^5-6x^2+10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"424\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-la-cotangente\"><\/span>\u5df2\u89e3\u51b3\u4f59\u5207\u7ebf\u5bfc\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u4f59\u5207\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-e1e391853b53d81ed500fd590799cbba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{cotg}(5x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/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-8581122adcd9d79db9862a27b57af0a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\text{cotg}(2x^4+10x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"236\" style=\"vertical-align: -5px;\"><\/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-e7814ccc95124c55f86b2f7036178254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f(x)=\\text{cotg}^5\\left(\\frac{x}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"160\" style=\"vertical-align: -12px;\"><\/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-1dcf8b02c8e9d9712210a78d116e2fc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{cotg}\\left(e^{x^2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"162\" style=\"vertical-align: -11px;\"><\/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-f358f9329696ee71ac2c1abfd5f9668e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\text{cotg}\\bigl(\\ln(x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"176\" style=\"vertical-align: -7px;\"><\/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-e26ae47cb88a301a3353d868fc9b74f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{cotg}\\left(\\sqrt{8x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"166\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b002740b34952198a8284265a444cbed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=-\\cfrac{5}{\\text{sen}^2(5x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"171\" style=\"vertical-align: -17px;\"><\/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-d9b86f549fab91f93d0fc4e437e1c4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=-\\cfrac{8x+10}{\\text{sen}^2(2x^4+10x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"257\" style=\"vertical-align: -17px;\"><\/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-eb1435fb7eb0c7bcff84741362417548_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f'(x)=5\\cdot \\text{cotg}^4\\left(\\frac{x}{2}\\right)\\cdot \\left(-\\frac{1}{\\text{sen}^2\\left(\\frac{x}{2}\\right)}\\right)\\cdot \\frac{1}{2}=-\\frac{5\\cdot \\text{cotg}^4\\left(\\frac{x}{2}\\right)}{2\\cdot \\text{sen}^2\\left(\\frac{x}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"468\" style=\"vertical-align: -23px;\"><\/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-4fb5fc0cea94ec46660b5bb16d9daaa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=-\\cfrac{2x\\cdot e^{x^2}}{\\text{sen}^2(e^{x^2})}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"175\" style=\"vertical-align: -18px;\"><\/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-efc6c63eb1a5cfc3f89deb4cfc3b4586_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=-\\cfrac{\\cfrac{2x}{x^2}}{\\text{sen}^2\\bigl(\\ln(x^2)\\bigr)}=-\\cfrac{2}{x\\cdot\\text{sen}^2\\bigl(\\ln(x^2)\\bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"356\" style=\"vertical-align: -20px;\"><\/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-70d6c7ac291ee53490646ae841842eef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=-\\cfrac{\\frac{8}{2\\sqrt{8x}}}{\\text{sen}^2\\left(\\sqrt{8x}\\right)}=-\\cfrac{4}{\\sqrt{8x}\\cdot \\text{sen}^2\\left(\\sqrt{8x}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"360\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-de-la-cotangente\"><\/span>\u4f59\u5207\u5bfc\u6570\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u6700\u540e\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u6f14\u793a\u4f59\u5207\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4ece\u4f59\u5207\u51fd\u6570\u7684\u6570\u5b66\u5b9a\u4e49\u5f00\u59cb\uff0c\u5b83\u7b49\u4e8e\u4f59\u5f26\u9664\u4ee5\u6b63\u5f26\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-dd85e2f7ac86aa67c6bd2f82fedfa926_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}(x)=\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"131\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u901a\u8fc7\u5e94\u7528\u5546\u7684\u5bfc\u6570\u89c4\u5219\u6765\u5bf9\u51fd\u6570\u8fdb\u884c\u5fae\u5206\uff1b <\/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-0eb90358967efc64de6d45b8eabe5e37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bigl(\\text{cotg}(x)\\bigr)'=\\left(\\frac{\\text{cos}(x)}{\\text{sen}(x)}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"181\" style=\"vertical-align: -17px;\"><\/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-7685acfe693a3c5e8dd2e543ad8ec7c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\text{sen}(x)\\cdot \\text{sen}(x)-\\text{cos}(x)\\cdot \\text{cos}(x) }{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"349\" style=\"vertical-align: -17px;\"><\/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-9988024649ed4fdb4b1a9bb913aa813f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\text{sen}^2(x)-\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"243\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u53d6\u5206\u6bcd\u4e2d\u7684\u516c\u56e0\u6570\u5e76\u4ece\u5206\u6570\u4e2d\u5220\u9664\u8d1f\u53f7\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-b23352ad101cdc7e1adeb6316c6d66c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=\\cfrac{-\\bigl(\\text{sen}^2(x)+\\text{cos}^2(x)\\bigr)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"259\" style=\"vertical-align: -17px;\"><\/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-df4c94284c00f257f7be601a98bf9475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{\\text{sen}^2(x)+\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"234\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u7531\u4e8e\u57fa\u672c\u7684\u4e09\u89d2\u6052\u7b49\u5f0f\uff0c\u6211\u4eec\u77e5\u9053\u6b63\u5f26\u7684\u5e73\u65b9\u52a0\u4e0a\u4f59\u5f26\u7684\u5e73\u65b9\u7b49\u4e8e 1\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-92d80771f891319379b2e756c5524aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(x)+\\text{cos}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\"><\/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-dd14ec817754afcafd5d862afc0703b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{1}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"157\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u7b2c\u4e00\u4e2a\u4f59\u5207\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u540c\u6837\uff0c\u4f59\u5272\u662f\u6b63\u5f26\u7684\u4e58\u6cd5\u5012\u6570\uff0c\u56e0\u6b64\u4e5f\u8bc1\u660e\u4e86\u4f59\u5207\u5bfc\u6570\u7684\u7b2c\u4e8c\u6761\u89c4\u5219\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-41aafad77ef896612fe6851ee97d914a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\text{sec}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e0a\u4e00\u6b65\u4e2d\u7684\u5206\u6570\u8f6c\u6362\u4e3a\u5206\u6570\u548c\u6765\u8bc1\u660e\u8be5\u4e09\u89d2\u51fd\u6570\u7684\u5bfc\u6570\u7684\u7b2c\u4e09\u4e2a\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-df4c94284c00f257f7be601a98bf9475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cotg}'(x)=-\\cfrac{\\text{sen}^2(x)+\\text{cos}^2(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"234\" style=\"vertical-align: -17px;\"><\/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-3780e44f1c85235473d47f418c7bc889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{cotg}'(x)=-\\left(\\frac{\\text{sen}^2(x)}{\\text{sen}^2(x)}+\\frac{\\text{cos}^2(x)}{\\text{sen}^2(x)}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"266\" style=\"vertical-align: -17px;\"><\/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-e7a8b05807749ddd4b8979253dcb2f45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=-\\bigl(1+\\text{cotg}^2(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"200\" style=\"vertical-align: -7px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u4f59\u5207\u503c\u3002\u60a8\u4f1a\u627e\u5230\u4f59\u5207\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u751a\u81f3\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u6211\u4eec\u8bc1\u660e\u4e86\u4f59\u5207\u5bfc\u6570 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%bd%99%e5%88%87%e5%80%bc%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\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-47","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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