{"id":389,"date":"2023-07-03T09:49:11","date_gmt":"2023-07-03T09:49:11","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e5%8f%8c%e6%9b%b2%e7%b7%9a%e9%80%86%e6%ad%a3%e6%8e%a5%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-07-03T09:49:11","modified_gmt":"2023-07-03T09:49:11","slug":"%e5%8f%8c%e6%9b%b2%e7%b7%9a%e9%80%86%e6%ad%a3%e6%8e%a5%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e5%8f%8c%e6%9b%b2%e7%b7%9a%e9%80%86%e6%ad%a3%e6%8e%a5%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u95a2\u6570\u306e\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u5c0e\u95a2\u6570\u306e\u89e3\u6c7a\u4f8b\u3082\u78ba\u8a8d\u3067\u304d\u3001\u6700\u5f8c\u306b\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-la-arcotangente-hiperbolica\"><\/span>\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u306e\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306f\u30011 \u306e 1 \u304b\u3089 x \u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u3082\u306e\u3067\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-33ae63a662489900a94430ce0dac1b60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{1-x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"413\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u95a2\u6570\u306e\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5fae\u5206\u5024\u306f\u3001<\/strong>\u305d\u306e\u95a2\u6570\u306e\u5fae\u5206\u5024\u3092 1 \u3067\u5272\u3063\u305f\u5546\u304b\u3089\u3001\u305d\u306e\u95a2\u6570\u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\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-3d5c743ab52bf834518230f3446aaa9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"413\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5b9f\u969b\u3001\u4e21\u65b9\u306e\u5f0f\u306f\u540c\u3058\u3067\u3059\u304c\u30012 \u756a\u76ee\u306e\u5f0f\u3067\u306f\u9023\u9396\u898f\u5247\u304c\u9069\u7528\u3055\u308c\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001x \u3092 u \u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001x \u306e\u5c0e\u95a2\u6570\u304c 1 \u3067\u3042\u308b\u305f\u3081\u3001\u6b63\u78ba\u306b\u6700\u521d\u306e\u5f0f\u304c\u5f97\u3089\u308c\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\/derivee-de-larctangente-hyperbolique.webp\" alt=\"\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\" class=\"wp-image-2343\" width=\"393\" height=\"298\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u9006\u6b63\u63a5\u304c\u6b63\u63a5\u306e\u9006\u95a2\u6570\u3067\u3042\u308b\u306e\u3068\u540c\u69d8\u306b\u3001\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306f\u53cc\u66f2\u7dda\u6b63\u63a5\u306e\u9006\u95a2\u6570\u3067\u3059\u3002\u305d\u308c\u3067\u3082\u3001\u305d\u308c\u3089\u306e\u5c0e\u95a2\u6570\u306f\u5927\u304d\u304f\u7570\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u4e09\u89d2\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f\u3053\u3053\u3067\u78ba\u8a8d\u3067\u304d\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\/\u53cc\u66f2\u7dda\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\/\">\u53cc\u66f2\u7dda\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-arcotangente-hiperbolica\"><\/span>\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\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-ad1cd9320973ca2c5d2b83434086f629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8ad6\u7406\u7684\u306b\u306f\u3001\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u6cd5\u5247\u3092\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-3d5c743ab52bf834518230f3446aaa9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"413\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> 2x \u306e\u5c0e\u95a2\u6570\u306f 2 \u306a\u306e\u3067\u3001\u5206\u6570\u306e\u5206\u5b50\u306b 2 \u3092\u5165\u308c\u3001\u5206\u6bcd\u306b 1 \u304b\u3089 2x \u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u3082\u306e\u3092\u5165\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-9820d63e99b4b29c41d6fd14a3426815_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{1-(2x)^2}}=\\cfrac{2}{1- 4x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"528\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u4f8b 2<\/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-3e4e12eb6cf782403fe0de4f37bc025f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(e^{3x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u89e3\u304f\u306b\u306f\u3001\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\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-3d5c743ab52bf834518230f3446aaa9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1-u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"413\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3055\u3089\u306b\u3001\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u5f15\u6570\u95a2\u6570\u306f\u8907\u5408\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u9023\u9396\u898f\u5247\u3082\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-0eb0da6a9477e040476051a829238c84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctanh}(e^{3x}) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{3\\cdot e^{3x}}{1-\\left(e^{3x}\\right)^2}=\\cfrac{3e^{3x}}{1-3^{6x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"534\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-de-la-arcotangente-hiperbolica\"><\/span>\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\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\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\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-17261fa2031302bfad1883eb39b7116d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arctanh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306f\u9006\u53cc\u66f2\u7dda\u6b63\u63a5\u3067\u3042\u308b\u305f\u3081\u3001\u524d\u306e\u7b49\u5f0f\u306f\u5225\u306e\u65b9\u6cd5\u3067\u8868\u73fe\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-27ba9a49fdc790b3131113b5ae592e2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{tanh}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b21\u306b\u3001\u65b9\u7a0b\u5f0f\u306e\u4e21\u8fba\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-4f8879b6d2f8df36bd6f3e5c817f21cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\cfrac{1}{\\text{cosh}^2(y)}\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"124\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p>\u79c1\u305f\u3061\u306f\u3042\u306a\u305f\u3092\u30af\u30ea\u30a2\u3057\u307e\u3059:<\/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-3bb09e461662267f0cbab52cf6e0bcac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\text{cosh}^2(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e00\u65b9\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u3068\u53cc\u66f2\u7dda\u6b63\u5f26\u306e\u4e8c\u4e57\u306e\u5dee\u306f 1 \u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u524d\u306e\u5f0f\u3092\u5206\u6570\u306b\u5909\u63db\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-e726904c011eb3ab9ff264426988d029_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(y)-\\text{senh}^2(y)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"183\" 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-1820ba4560d8d0109af605b6e2757c93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\text{cosh}^2(y)}{1}=\\cfrac{\\text{cosh}^2(y)}{\\text{cosh}^2(y)-\\text{senh}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"281\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u306e\u3059\u3079\u3066\u306e\u9805\u3092\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u4e8c\u4e57\u3067\u5272\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-9cc80abe73f130f4ec1c39cbf5d7e8ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\cfrac{\\text{cosh}^2(y)}{\\text{cosh}^2(y)}}{\\cfrac{\\text{cosh}^2(y)}{\\text{cosh}^2(y)}-\\cfrac{\\text{senh}^2(y)}{\\text{cosh}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"101\" width=\"195\" style=\"vertical-align: -46px;\"><\/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-b150bbe95858decf7312b869b95d24b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{1-\\cfrac{\\text{senh}^2(y)}{\\text{cosh}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"138\" style=\"vertical-align: -46px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u9593\u306e\u53cc\u66f2\u7dda\u6b63\u5f26\u306e\u5546\u306f\u53cc\u66f2\u7dda\u6b63\u63a5\u306b\u7b49\u3057\u3044\u306e\u3067\u3001\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-12f286528bc0635705aadbe510b6ceb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}(x)=\\cfrac{\\text{senh}(x)}{\\text{cosh}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"144\" 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-725424805ce03fcabd470e9448c91f2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{1-\\text{tanh}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"136\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p>\u3057\u304b\u3057\u3001\u8a3c\u660e\u306e\u6700\u521d\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u53cc\u66f2\u7dda\u6b63\u63a5\u306f\u5909\u6570 x \u3068\u540c\u7b49\u3067\u3042\u308b\u305f\u3081\u3001\u5f0f\u3092\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u53cc\u66f2\u7dda\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u5f0f\u304c\u5f97\u3089\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-b90ecc88a8cbc7f110840727da48e632_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{1-x^2}\" 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