{"id":47,"date":"2023-09-17T10:54:18","date_gmt":"2023-09-17T10:54:18","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-09-17T10:54:18","modified_gmt":"2023-09-17T10:54:18","slug":"%e3%82%b3%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3084\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\u6f14\u7fd2\u3082\u898b\u3064\u304b\u308a\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cotangente\"><\/span>\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u306e\u4f59\u63a5\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u6b63\u5f26\u306e 2 \u4e57\u306e\u8ca0\u306e 1 \u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/strong> x \u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u3082\u306e\u3001\u304a\u3088\u3073 1 \u3068 x \u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e 2 \u4e57\u3092\u8db3\u3057\u305f\u5408\u8a08\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\u3082\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\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>\u5f15\u6570\u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u304c x \u4ee5\u5916\u306e\u95a2\u6570\u3067\u3042\u308b\u5834\u5408\u3001\u95a2\u6570\u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u5f0f\u306f\u524d\u306e\u5f0f\u3068\u540c\u3058\u3067\u3059\u304c\u3001\u5f0f\u306b\u5f15\u6570\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u4e57\u7b97\u3057\u307e\u3059\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> \u3053\u308c\u306f\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u305f\u3081\u306e 3 \u3064\u306e\u7570\u306a\u308b\u516c\u5f0f\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u8ad6\u7406\u7684\u306b\u306f\u30013 \u3064\u306e\u516c\u5f0f\u3092\u3059\u3079\u3066\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u306f\u306a\u304f\u3001\u597d\u307f\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\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=\"\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u304b\u3089\u5c0e\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>\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u95a2\u6570\u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u898b\u3066\u304d\u305f\u306e\u3067\u3001\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u89e3\u304d\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cotangente-de-2x\"><\/span>\u4f8b 1: 2x \u306e\u4f59\u63a5\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u95a2\u6570 2x \u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u304c\u4f55\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\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>\u3053\u308c\u307e\u3067\u898b\u3066\u304d\u305f\u3088\u3046\u306b\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u4e0a\u8a18\u306e 3 \u3064\u306e\u516c\u5f0f\u306e\u3044\u305a\u308c\u304b\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u6b63\u5f26\u6ce2\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u307e\u3059\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-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> 2x \u306f 1 \u6b21\u9805\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u5c0e\u95a2\u6570\u306f 2 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012x \u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306f\u30012x \u306e\u6b63\u5f26\u306e 2 \u4e57\u3067\u5272\u3063\u305f\u8ca0\u306e 2 \u306b\u306a\u308a\u307e\u3059\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-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>\u4f8b 2: x \u306e 2 \u4e57\u306e\u4f59\u63a5\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>2 \u756a\u76ee\u306e\u4f8b\u3067\u306f\u3001x \u306e 2 \u4e57\u306e\u4f59\u63a5\u306e\u5c0e\u95a2\u6570\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u6c7a\u5b9a\u3057\u307e\u3059\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>\u3053\u306e\u4f8b\u3067\u306f\u3001\u4f59\u63a5\u5f15\u6570\u306e\u95a2\u6570\u306f x \u3067\u306f\u306a\u3044\u305f\u3081\u3001\u9023\u9396\u898f\u5247\u3092\u9069\u7528\u3057\u3066\u4f59\u63a5\u3092\u5fae\u5206\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\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 \u306e 2 \u4e57\u306e\u5c0e\u95a2\u6570\u306f 2x \u3067\u3042\u308b\u305f\u3081\u3001x <sup>2<\/sup>\u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/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>\u4f8b 3: \u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e 3 \u4e57\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6700\u5f8c\u306b\u3001\u591a\u9805\u5f0f\u95a2\u6570\u306e\u4f59\u63a5\u306e 3 \u4e57\u306e\u5c0e\u95a2\u6570\u306f\u3044\u304f\u3089\u304b\u3092\u6c42\u3081\u307e\u3059\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-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>\u3053\u306e\u5834\u5408\u3001\u95a2\u6570\u306e\u5408\u6210\u304c\u3042\u308b\u305f\u3081\u3001\u4f59\u63a5\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u306e\u5f0f\u3067\u9023\u9396\u5f8b\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/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>\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5fae\u5206\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u4f59\u63a5\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\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-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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/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>\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u8a3c\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u306e\u6700\u5f8c\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u95a2\u6570\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u304b\u3089\u59cb\u3081\u307e\u3059\u3002\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u95a2\u6570\u306f\u3001\u30b3\u30b5\u30a4\u30f3\u3092\u30b5\u30a4\u30f3\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u7b49\u3057\u3044\u3067\u3059\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-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>\u3053\u3053\u3067\u3001\u5546\u306e\u5c0e\u95a2\u6570\u306e\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3057\u3066\u95a2\u6570\u3092\u5fae\u5206\u3057\u307e\u3059\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-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>\u5206\u6bcd\u306e\u5171\u901a\u56e0\u6570\u3092\u3068\u308a\u3001\u5206\u6570\u304b\u3089\u8ca0\u306e\u7b26\u53f7\u3092\u53d6\u308a\u9664\u304d\u307e\u3059\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-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>\u4e00\u65b9\u3001\u57fa\u672c\u7684\u306a\u4e09\u89d2\u95a2\u6570\u306e\u6052\u7b49\u6027\u306e\u304a\u304b\u3052\u3067\u3001\u30b5\u30a4\u30f3\u306e 2 \u4e57\u3068\u30b3\u30b5\u30a4\u30f3\u306e 2 \u4e57\u3092\u8db3\u3057\u305f\u3082\u306e\u306f 1 \u306b\u7b49\u3057\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u307e\u3059\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>\u3053\u3046\u3057\u3066\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u6700\u521d\u306e\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u3002\u540c\u69d8\u306b\u3001\u30b3\u30bb\u30ab\u30f3\u30c8\u306f\u30b5\u30a4\u30f3\u306e\u9006\u4e57\u3067\u3042\u308b\u305f\u3081\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e 2 \u756a\u76ee\u306e\u898f\u5247\u3082\u8a3c\u660e\u3055\u308c\u307e\u3059\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-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\u5f8c\u306b\u3001\u3053\u306e\u4e09\u89d2\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e 3 \u756a\u76ee\u306e\u516c\u5f0f\u306f\u3001\u524d\u306e\u30b9\u30c6\u30c3\u30d7\u306e\u5206\u6570\u3092\u5206\u6570\u306e\u5408\u8a08\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u8a3c\u660e\u3067\u304d\u307e\u3059\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-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>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3084\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\u6f14\u7fd2\u3082\u898b\u3064\u304b\u308a\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002 \u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f x \u306e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570<\/span> \u3082\u3063\u3068\u8aad\u3080 &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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