{"id":390,"date":"2023-07-03T07:22:34","date_gmt":"2023-07-03T07:22:34","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%bb%e3%82%ab%e3%83%b3%e3%83%88%e3%81%8b%e3%82%89%e5%b0%8e%e5%87%ba%e3%81%95%e3%82%8c%e3%81%be%e3%81%99\/"},"modified":"2023-07-03T07:22:34","modified_gmt":"2023-07-03T07:22:34","slug":"%e3%82%b3%e3%82%bb%e3%82%ab%e3%83%b3%e3%83%88%e3%81%8b%e3%82%89%e5%b0%8e%e5%87%ba%e3%81%95%e3%82%8c%e3%81%be%e3%81%99","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%bb%e3%82%ab%e3%83%b3%e3%83%88%e3%81%8b%e3%82%89%e5%b0%8e%e5%87%ba%e3%81%95%e3%82%8c%e3%81%be%e3%81%99\/","title":{"rendered":"\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\uff08\u5f0f\uff09\u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u7df4\u7fd2\u554f\u984c\u3082\u898b\u3064\u304b\u308a\u307e\u3059\u3002\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-cosecante\"><\/span>\u30b3\u30bb\u30ab\u30f3\u30c8\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u306e\u4f59\u5272\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u4f59\u5f26\u3092 x \u306e\u4e8c\u4e57\u6b63\u5f26\u3067\u5272\u3063\u305f\u5546\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\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-19e966c85664331b8b6c87860849678d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"416\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4e09\u89d2\u95a2\u6570\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001x \u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u3001x \u306e\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u3068 x \u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u7a4d\u3092\u5f15\u3044\u305f\u3082\u306e\u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3082\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-e66d4cc483a3f2c40401bf2e34fa54c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}=-\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\\cdot \\cfrac{1}{\\text{sen}(x)}=-\\text{cot}(x)\\cdot \\text{cosec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u9023\u9396\u5247\u3092\u9069\u7528\u3059\u308b\u3068\u3001<strong>\u95a2\u6570\u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5fae\u5206\u5024<\/strong>\u306f\u3001\u95a2\u6570\u306e\u5fae\u5206\u5024\u3068\u95a2\u6570\u306e\u30b3\u30b5\u30a4\u30f3\u306e\u7a4d\u3092\u6e1b\u7b97\u3057\u3001\u95a2\u6570\u306e\u6b63\u5f26\u306e 2 \u4e57\u3067\u5272\u3063\u305f\u5024\u306b\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u3092\u5c0e\u51fa\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\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\/derive-de-la-formule-cosecante.webp\" alt=\"\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u516c\u5f0f\u304b\u3089\u5c0e\u304d\u51fa\u3055\u308c\u308b\" class=\"wp-image-2527\" width=\"398\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cosecante\"><\/span>\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u306e\u3067\u3001\u6b21\u306b\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u306e\u4f59\u5272\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u304b\u3092\u6b63\u78ba\u306b\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cosecante-de-2x\"><\/span>\u4f8b 1: 2x \u306e\u4f59\u5272\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u30012x \u306e\u4f59\u5272\u306e\u5fae\u5206\u304c\u3069\u306e\u304f\u3089\u3044\u306b\u306a\u308b\u304b\u3092\u78ba\u8a8d\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-44aef07389e7b7d69f4ecf9e46660838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u30b3\u30bb\u30ab\u30f3\u30c8\u5f15\u6570\u95a2\u6570\u306f x \u3068\u306f\u7570\u306a\u308b\u305f\u3081\u3001\u30b3\u30bb\u30ab\u30f3\u30c8\u5fae\u5206\u898f\u5247\u3068\u9023\u9396\u898f\u5247\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u4e09\u89d2\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u524d\u306e\u5f0f\u306e\u5024\u3092\u5358\u7d14\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002\u30b3\u30b5\u30a4\u30f3\u3068\u30b5\u30a4\u30f3\u306e\u5f15\u6570\u306b 2x \u3092\u5165\u529b\u3057\u3001u&#8217; \u306f 2x \u306e\u5c0e\u95a2\u6570\u3001\u3064\u307e\u308a 2 \u306b\u5bfe\u5fdc\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-8607025c53ca3c1a2c5e05e908d61bc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2\\cdot \\text{cos}(2x)}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cosecante-de-x-al-cuadrado\"><\/span>\u4f8b 2: x \u306e 2 \u4e57\u306e\u4f59\u5272\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u3053\u306e\u6f14\u7fd2\u3067\u306f\u3001x \u306e 2 \u4e57\u306e\u4f59\u5272\u306e\u5c0e\u95a2\u6570\u304c\u3069\u306e\u304f\u3089\u3044\u306b\u306a\u308b\u304b\u3092\u78ba\u8a8d\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-dc9de51c8f24850940b40de616428dd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8ad6\u7406\u7684\u306b\u306f\u3001\u3053\u306e\u4e09\u89d2\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f\u3001\u4f59\u5272\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> x \u306e 2 \u4e57\u306e\u5c0e\u95a2\u6570\u306f 2x \u3068\u306a\u308b\u305f\u3081\u3001x \u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u306e 2 \u4e57\u306e\u5c0e\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\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-0a6b69e1f9851904ec2fc68bffeedc64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x\\cdot \\text{cos}(x^2)}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"454\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-cosecante-al-cubo-de-una-funcion-exponencial\"><\/span>\u4f8b 3: \u6307\u6570\u95a2\u6570\u306e 3 \u4e57\u4f59\u5272\u306e\u5c0e\u95a2\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-8bd5c47e8cd53ab52d3d30f55f898490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}^3(e^{5x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u95a2\u6570\u306e\u5f15\u6570\u304c\u4f55\u3067\u3042\u3063\u3066\u3082\u3001\u95a2\u6570\u306e\u4f59\u5272\u306e\u5c0e\u95a2\u6570\u306e\u898f\u5247\u306f\u6b21\u306e\u3068\u304a\u308a\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3057\u304b\u3057\u3001\u3053\u306e\u5834\u5408\u3001\u30b3\u30bb\u30ab\u30f3\u30c8\u304c 3 \u306b\u7d2f\u4e57\u3055\u308c\u3001\u3055\u3089\u306b\u305d\u306e\u5f15\u6570\u306b\u6307\u6570\u95a2\u6570\u304c\u3042\u308b\u305f\u3081\u3001\u8907\u5408\u95a2\u6570\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u5168\u4f53\u3092\u533a\u5225\u3059\u308b\u306b\u306f\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u6570\u56de\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\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-9ac2ce49dfcba1b7f27696dba0a2decb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle f'(x)&amp; = 3\\text{cosec}^2(e^{5x})\\cdot\\left(-\\frac{5e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\right)\\\\[1.5ex]&amp;=-\\frac{-15\\text{cosec}^2(e^{5x})\\cdot e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-la-cosecante\"><\/span>\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u4f59\u5272\u95a2\u6570\u3092\u5c0e\u51fa\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-9929e2437b0ed56c3510e3e0e66745c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{cosec}(x^4-2x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"203\" 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-90abcf0539f30dc6fc72414bfc74510f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{cosec}(x^3+e^x-10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"232\" 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-86a2ea6229cced9086f8baba7afd49dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{cosec}\\bigl(\\ln(x^3+7x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" 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-45cdf124149223f4a3bec4984dc3ad3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{cosec}\\bigl(\\text{arccos}(x^7)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"217\" 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-45ae6ef998d8ab0c30309fe521b0bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{cosec}\\left(\\sqrt{9x^2-4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"226\" style=\"vertical-align: -11px;\"><\/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\u53c2\u7167<\/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-1fb207498fc67f62e6c30a0baecc9549_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f('x)=-\\cfrac{(4x^3-4x)\\cdot \\text{cos}(x^4-2x^2)}{\\text{sen}^2(x^4-2x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"303\" 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-d42a3db78890f44f3cac95685ab9362e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f('x)=-\\cfrac{(3x^2+e^x)\\cdot \\text{cos}(x^3+e^x-10)}{\\text{sen}^2(x^3+e^x-10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"329\" 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-32dde68d2a11ef6a05d483b26f0a98ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp; =-\\cfrac{\\cfrac{3x^2+14x}{x^3+7x^2}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{\\cfrac{3x+14}{x^2+7x}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{(3x+14)\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{(x^2+7x)\\cdot \\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"333\" style=\"vertical-align: 0px;\"><\/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-b2bea25dae467cefdcc1bd48e8d9bc88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp; =-\\cfrac{-\\cfrac{7x^6}{\\sqrt{1-\\left(x^7\\right)^2}}\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =-\\cfrac{(-7x^6)\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =\\cfrac{7x^6\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"240\" width=\"348\" style=\"vertical-align: 0px;\"><\/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-eb70e1d7b6f2ce2636934b235904861f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\text{E) }f'(x)&amp; =-\\cfrac{\\cfrac{18x-4}{2\\cdot\\sqrt{9x^2-4x}} \\cdot \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{\\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)}\\\\[1.5ex] &amp;=-\\cfrac{(18x-4)\\cdot  \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{2\\sqrt{9x^2-4x}\\cdot \\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"165\" width=\"352\" style=\"vertical-align: 0px;\"><\/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-formula-de-la-derivada-de-la-cosecante\"><\/span>\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u8a3c\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306b\u3001\u4f59\u5272\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002\u4ed6\u306e\u30c7\u30e2\u3068\u306f\u7570\u306a\u308a\u3001\u3053\u306e\u5834\u5408\u306f\u5c0e\u95a2\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u5236\u9650\u3092\u4f7f\u7528\u3057\u307e\u305b\u3093\u304c\u3001\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u304b\u3089\u59cb\u3081\u307e\u3059\u3002<\/p>\n<p>\u4ee3\u6570\u7684\u306b\u306f\u3001\u4f59\u5272\u4e09\u89d2\u95a2\u6570\u306f\u6b63\u5f26\u306e\u4e57\u6cd5\u9006\u95a2\u6570\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-6ac8ff987dcebfb971915b090d8dc455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x)=\\cfrac{1}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"196\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5546\u898f\u5247\u3092\u4f7f\u7528\u3057\u3066\u4f59\u5272\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\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-956e802336ed97943a839dbc059a168a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{0\\cdot \\text{sen}(x)-1\\cdot \\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"227\" 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-d26ab733704d285da0ec63f0901330b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{-\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u5272\u308a\u7b97\u306e\u5c0e\u95a2\u6570\u306e\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u306e\u307f\u3001\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306b\u5230\u9054\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u5546\u306e\u5c0e\u95a2\u6570\u306f\u3059\u3067\u306b\u8a3c\u660e\u3055\u308c\u3066\u3044\u308b\u305f\u3081 (\u6b21\u306e\u30ea\u30f3\u30af\u3067\u78ba\u8a8d\u3067\u304d\u307e\u3059)\u3001\u30b3\u30bb\u30ab\u30f3\u30c8\u5c0e\u95a2\u6570\u5247\u3082\u8a3c\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u9664\u7b97\u5546\u306e\u5c0e\u95a2\u6570\/\">\u5546\u306e\u5c0e\u95a2\u6570\u306e\u8a3c\u660e<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\uff08\u5f0f\uff09\u306e\u30b3\u30bb\u30ab\u30f3\u30c8\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u30b3\u30bb\u30ab\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u7df4\u7fd2\u554f\u984c\u3082\u898b\u3064\u304b\u308a\u307e\u3059\u3002\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u30b3\u30bb\u30ab\u30f3\u30c8 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%bb%e3%82%ab%e3%83%b3%e3%83%88%e3%81%8b%e3%82%89%e5%b0%8e%e5%87%ba%e3%81%95%e3%82%8c%e3%81%be%e3%81%99\/\"> <span class=\"screen-reader-text\">\u30b3\u30bb\u30ab\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-390","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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