{"id":385,"date":"2023-07-03T14:10:00","date_gmt":"2023-07-03T14:10:00","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e5%8f%8c%e6%9b%b2%e7%b7%9a%e4%bd%99%e5%bc%a6%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-07-03T14:10:00","modified_gmt":"2023-07-03T14:10:00","slug":"%e5%8f%8c%e6%9b%b2%e7%b7%9a%e4%bd%99%e5%bc%a6%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%e4%bd%99%e5%bc%a6%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u793a\u3057\u3001\u6700\u5f8c\u306b\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\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-del-coseno-hiperbolico\"><\/span>\u53cc\u66f2\u7dda\u4f59\u5f26\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u53cc\u66f2\u7dda\u6b63\u5f26\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-2c3935efe4db8dd3b7852cc93509c06c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"394\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u95a2\u6570\u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u3001<\/strong>\u95a2\u6570\u306e\u53cc\u66f2\u7dda\u6b63\u5f26\u3068\u305d\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u7a4d\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-764d8e891bc33a54d2ad73393df144c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 2 \u756a\u76ee\u306e\u5f0f\u306f\u6700\u521d\u306e\u5f0f\u3068\u540c\u3058\u3067\u3059\u304c\u3001\u552f\u4e00\u306e\u9055\u3044\u306f\u30012 \u756a\u76ee\u3067\u306f\u9023\u9396\u30eb\u30fc\u30eb\u304c\u9069\u7528\u3055\u308c\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306e\u5f0f\u306f x \u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u3092\u5c0e\u51fa\u3059\u308b\u305f\u3081\u306b\u306e\u307f\u4f7f\u7528\u3067\u304d\u307e\u3059\u304c\u30012 \u756a\u76ee\u306e\u5f0f\u306f\u3042\u3089\u3086\u308b\u30bf\u30a4\u30d7\u306e\u95a2\u6570\u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u3092\u5c0e\u51fa\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\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-du-cosinus-hyperbolique.webp\" alt=\"\" class=\"wp-image-2064\" width=\"427\" height=\"278\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u53cc\u66f2\u7dda\u30b3\u30b5\u30a4\u30f3\u306e\u5fae\u5206\u306e\u516c\u5f0f\u306f\u30b3\u30b5\u30a4\u30f3\u306e\u5fae\u5206\u306e\u516c\u5f0f\u3068\u306f\u7570\u306a\u308a\u307e\u3059\u304c\u3001\u3044\u304f\u3064\u304b\u306e\u985e\u4f3c\u70b9\u304c\u3042\u308a\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\/\u30b3\u30b5\u30a4\u30f3\u304b\u3089\u5c0e\u51fa\u3055\u308c\u307e\u3059\/\">\u30b3\u30b5\u30a4\u30f3\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-del-coseno-hiperbolico\"><\/span>\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u4ee5\u4e0b\u3067\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\u8cea\u554f\u304c\u3042\u308c\u3070\u30b3\u30e1\u30f3\u30c8\u3067\u8cea\u554f\u3067\u304d\u308b\u3053\u3068\u3092\u5fd8\u308c\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-coseno-hiperbolico-de-2x\"><\/span>\u4f8b 1: 2x \u306e\u53cc\u66f2\u7dda\u4f59\u5f26\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-6c79bebc7f8b263bee01848f5babea49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5f15\u6570\u306b x \u3068\u306f\u7570\u306a\u308b\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u9023\u9396\u5f8b\u306b\u3088\u308b\u53cc\u66f2\u7dda\u4f59\u5f26\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-764d8e891bc33a54d2ad73393df144c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 2x \u306e\u5c0e\u95a2\u6570\u306f 2 \u3067\u3042\u308b\u305f\u3081\u30012x \u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u30012x \u306b 2 \u3092\u639b\u3051\u305f\u53cc\u66f2\u7dda\u6b63\u5f26\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-b84c1d5aa09cb545408a723b54f8fbf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(2x)\\cdot 2=2\\text{cosh}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"533\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-coseno-hiperbolico-de-x-al-cuadrado\"><\/span>\u4f8b 2: x \u306e 2 \u4e57\u306e\u53cc\u66f2\u7dda\u4f59\u5f26\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-daf8b19f319b047a8b677ff1f158cd16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"122\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e0a\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u95a2\u6570\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-764d8e891bc33a54d2ad73393df144c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u4e00\u65b9\u3067\u306f 2x \u3092\u4e0e\u3048\u308b\u4e8c\u6b21\u95a2\u6570 x <sup>2<\/sup>\u3092\u5c0e\u51fa\u3057\u3001\u6b21\u306b\u95a2\u6570\u5168\u4f53\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-3f15e7e138793e4cdcb3da8a84724d5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{senh}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"443\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-del-coseno-hiperbolico\"><\/span>\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u8a3c\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u304c\u3069\u3053\u304b\u3089\u6765\u305f\u306e\u304b\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5f0f\u304b\u3089\u59cb\u3081\u308b\u3068\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-441432af7fa8c1db95476b9541e222d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x)=\\cfrac{e^x+e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5f0f\u306e\u4e21\u5074\u304b\u3089\u6b21\u306e\u3088\u3046\u306b\u63a8\u6e2c\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-5ace35f9bdf59afdfd1dc06cccade202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bigl(\\text{cosh}(x)\\bigr)'=\\left(\\frac{e^x+e^{-x}}{2}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"200\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u53f3\u5074\u306b\u306f\u5272\u308a\u7b97\u304c\u3042\u308b\u306e\u3067\u3001\u5546\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u9069\u7528\u3057\u3066\u5c0e\u95a2\u6570\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-dacf4babd2368ad5d84913142cd1c988_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}'(x)=\\frac{(e^x-e^{-x})\\cdot 2}{2^2}=\\frac{e^x-e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"283\" style=\"vertical-align: -12px;\"><\/p>\n<\/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\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u30eb\u30fc\u30eb<\/a><\/span><\/p>\n<p>\u3088\u304f\u898b\u308b\u3068\u3001\u5f97\u3089\u308c\u305f\u5f0f\u306f\u53cc\u66f2\u7dda\u6b63\u5f26\u306e\u5f0f\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u7b49\u5f0f\u304c\u7b49\u4fa1\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\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-9fafe72628e85aed5276d0a6b9104baa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}'(x)=\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"143\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u6cd5\u5247\u306b\u5230\u9054\u3057\u3001\u305d\u308c\u304c\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u793a\u3057\u3001\u6700\u5f8c\u306b\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002 \u53cc\u66f2\u7dda\u4f59\u5f26\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u5f0f x \u306e\u53cc\u66f2\u7dda\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u53cc\u66f2\u7dda\u6b63\u5f26\u3067 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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