{"id":383,"date":"2023-07-03T16:46:24","date_gmt":"2023-07-03T16:46:24","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%83%a9%e3%83%ab%e3%82%b3%e3%82%b7%e3%83%b3%e8%aa%98%e5%b0%8e%e4%bd%93-2\/"},"modified":"2023-07-03T16:46:24","modified_gmt":"2023-07-03T16:46:24","slug":"%e3%83%a9%e3%83%ab%e3%82%b3%e3%82%b7%e3%83%b3%e8%aa%98%e5%b0%8e%e4%bd%93-2","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%83%a9%e3%83%ab%e3%82%b3%e3%82%b7%e3%83%b3%e8%aa%98%e5%b0%8e%e4%bd%93-2\/","title":{"rendered":"\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u95a2\u6570\u306e\u9006\u4f59\u5f26\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3082\u3042\u308a\u3001\u6bb5\u968e\u7684\u306b\u89e3\u3044\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u30a2\u30fc\u30af\u30b3\u30b5\u30a4\u30f3\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcocoseno\"><\/span>\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>x \u306e\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u30011 \u304b\u3089 x \u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u5024\u306e\u5e73\u65b9\u6839\u3092\u8ca0\u306e 1 \u3067\u8a08\u7b97\u3057\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-08ccbc72f9a1b83be4c2d4ce41e7f10e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u95a2\u6570\u306e\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u3001<\/strong>\u305d\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092 1 \u304b\u3089\u305d\u306e\u95a2\u6570\u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u5e73\u65b9\u6839\u3067\u5272\u3063\u305f\u5546\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u5b9f\u969b\u3001\u6700\u521d\u306e\u5f0f\u306f\u30012 \u756a\u76ee\u306e\u5f0f\u306e x \u3092 u \u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002\u8981\u7d04\u3059\u308b\u3068\u3001\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\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-arc-cosinus.webp\" alt=\"\u9006\u4f59\u5f26\u5c0e\u95a2\u6570\" class=\"wp-image-1973\" width=\"432\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001 arccosine \u306e\u5c0e\u95a2\u6570\u306e\u5f0f\u306f<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u30e9\u30eb\u30b3\u30b7\u30f3\u8a98\u5c0e\u4f53\/\">arcsine \u306e\u5c0e\u95a2\u6570<\/a><\/span>\u306b\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u305d\u306e\u524d\u306b\u8ca0\u306e\u5024\u304c\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocoseno\"><\/span>\u9006\u4f59\u5f26\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u9006\u4f59\u5f26\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u304c\u4e0e\u3048\u3089\u308c\u305f\u306e\u3067\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u5c0e\u95a2\u6570\u306e\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u5206\u6790\u3057\u307e\u3059\u3002\u3053\u3046\u3059\u308b\u3053\u3068\u3067\u3001\u95a2\u6570\u306e\u9006\u4f59\u5f26\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u306e\u304b\u3092\u7406\u89e3\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcocoseno-de-2x\"><\/span>\u4f8b 1: 2x \u306e\u9006\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-c913be328da0f829a3545ccf101e15e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u3092\u89e3\u304f\u306b\u306f\u3001\u6b21\u306e\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> 2x \u306e\u5fae\u5206\u5024\u306f 2 \u3067\u3042\u308b\u305f\u3081\u30012x \u306e\u9006\u4f59\u5f26\u5fae\u5206\u5024\u306f\u3001\u30eb\u30fc\u30c8 1 \u304b\u3089 2x \u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u5024\u304b\u3089\u30de\u30a4\u30ca\u30b9 2 \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-cf892a94fcba0edb3ae5c4d8ff013899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\sqrt{1-(2x)^2}}=-\\cfrac{2}{\\sqrt{1-4x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"576\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcocoseno-de-x-al-cuadrado\"><\/span>\u4f8b 2: x \u306e 2 \u4e57\u306e\u9006\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-b2f6ac6474aa61a7eddba4bb79a45ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u9006\u4f59\u5f26\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u9023\u9396\u5247\u306b\u9069\u7528\u3057\u3066\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u95a2\u6570 x <sup>2<\/sup>\u306e\u5c0e\u95a2\u6570\u306f 2x \u3067\u3042\u308b\u305f\u3081\u3001x \u306e\u9006\u4f59\u5f26\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-e9180f04fd27262ca57f4b648c3b6b9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\sqrt{1-\\left(x^2\\right)^2}}=-\\cfrac{2x}{\\sqrt{1-x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"565\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcocoseno-de-un-logaritmo\"><\/span>\u4f8b 3: \u5bfe\u6570\u306e\u9006\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-d172240febea273fb3978225f13eebad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u306e\u95a2\u6570\u306f\u9006\u4f59\u5f26\u3068\u81ea\u7136\u5bfe\u6570\u304b\u3089\u69cb\u6210\u3055\u308c\u308b\u95a2\u6570\u306a\u306e\u3067\u3001\u9023\u9396\u5f8b\u3092\u4f7f\u7528\u3057\u3066\u5c0e\u51fa\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u81ea\u7136\u5bfe\u6570\u306e\u5c0e\u95a2\u6570\u306f x \u3067\u5272\u3063\u305f\u3082\u306e\u3067\u3042\u308b\u305f\u3081\u3001\u6574\u6570\u95a2\u6570\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-d682371fc7d064383f30416a40a4f9ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\cfrac{1}{x}}{\\sqrt{1-\\left(\\ln(x)\\right)^2}}=\\cfrac{1}{x\\sqrt{1-\\ln^2(x)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"582\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcocoseno\"><\/span>\u9006\u4f59\u5f26\u5c0e\u95a2\u6570\u3067\u554f\u984c\u304c\u89e3\u6c7a\u3055\u308c\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u9006\u4f59\u5f26\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-35e2715201a91cea5d5a914619695b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arccos}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" 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-a2bc15a65a4f4e6c42effc3e21437657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arccos}(x^3+6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-38ed3b9ec0b9a3cb6443dec0c6afb6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arccos}^3\\left(e^{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" 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-766af35119810145dd3589fab05d2f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arccos}\\left(\\log_3(x^3)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" 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-ce6b5d78ea798a70c51759cce27e5b25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arccos}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"181\" 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\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-79dbfad4db01cc46534b4875a7a8c905_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=-\\cfrac{7}{\\sqrt{1-(7x)^2}}=-\\cfrac{7}{\\sqrt{1-49x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"314\" 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-fd07daef79650fcb34116e266aee09fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=-\\cfrac{3x^2+6}{\\sqrt{1-(x^3+6x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"233\" 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-0ffd255c55afc3967dc250bc63741575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }\\displaystyle f'(x)&amp;=3\\text{arccos}^2\\left(e^{3x}\\right)\\cdot \\left(-\\frac{3e^{3x}}{\\sqrt{1-\\left(e^{3x}\\right)^2}}\\right)\\\\[1.5ex] &amp;=-\\cfrac{9\\text{arccos}^2\\left(e^{3x}\\right)\\cdot e^{3x}}{\\sqrt{1-e^{6x}}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"131\" width=\"346\" 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-ec25311613f0552bbc52d2d15581d3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp;=-\\cfrac{1}{\\sqrt{1-\\left(\\log_3(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 3}\\\\[1.5ex] &amp;=-\\cfrac{1}{x\\cdot \\ln 3\\cdot \\sqrt{1-\\log_3^2(3x)}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"312\" 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-d1a362c38a56084dec3c6ebbccba9ab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) } f'(x)&amp; =-\\cfrac{1}{\\sqrt{1-\\left(\\sqrt{4x}\\right)^2}}\\cdot \\cfrac{4}{2\\sqrt{4x}}\\\\[1.5ex] &amp;=-\\cfrac{2}{\\sqrt{1-4x}\\cdot 2\\sqrt{x}}\\\\[1.5ex] &amp;=-\\cfrac{1}{\\sqrt{x-4x^2}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"184\" width=\"267\" 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-del-arcocoseno\"><\/span>\u9006\u4f59\u5f26\u5fae\u5206\u516c\u5f0f\u306e\u8a3c\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u30a2\u30fc\u30af\u30b3\u30b5\u30a4\u30f3\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-0a3001135fdded9698f51b8a683036c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arccos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u307e\u305a\u3001\u30a2\u30fc\u30af\u30b3\u30b5\u30a4\u30f3\u3092\u30b3\u30b5\u30a4\u30f3\u306b\u5909\u63db\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-32b94bb993d1256aa9088d9bffbb0941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{cos}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u7b49\u5f0f\u306e 2 \u3064\u306e\u8fba\u3092\u63a8\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-e5f229f3e26b190eca429017bd78dba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=-\\text{sen}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u79c1\u305f\u3061\u306f\u3042\u306a\u305f\u3092\u30af\u30ea\u30a2\u3057\u307e\u3059\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-b2c2f95f5c7999d81cd10976320a7413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\text{sen}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u57fa\u672c\u7684\u306a\u4e09\u89d2\u95a2\u6570\u6052\u7b49\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u30b5\u30a4\u30f3\u3092\u30b3\u30b5\u30a4\u30f3\u306b\u5909\u66f4\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-9af2ef5387e227b363035275ba0777e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{sen}(y)=\\sqrt{1-\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"390\" style=\"vertical-align: -6px;\"><\/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-3c3807ba3700aac7694b04356a9a25d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"157\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u3057\u304b\u3057\u3001\u4e0a\u3067 x \u304c y \u306e\u30b3\u30b5\u30a4\u30f3\u306b\u7b49\u3057\u3044\u3068\u63a8\u5b9a\u3057\u305f\u305f\u3081\u3001\u65b9\u7a0b\u5f0f\u306f\u6b8b\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-8c3b21ba43e58ec763ab27498aa4fb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"117\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u5f0f\u306b\u5230\u9054\u3057\u305f\u306e\u3067\u3001\u305d\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\u95a2\u6570\u306e\u9006\u4f59\u5f26\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3082\u3042\u308a\u3001\u6bb5\u968e\u7684\u306b\u89e3\u3044\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u30a2\u30fc\u30af\u30b3\u30b5\u30a4\u30f3\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u3092\u793a\u3057\u307e\u3059\u3002 \u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306f\u4f55\u3067\u3059\u304b? x \u306e\u9006\u4f59\u5f26\u306e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%83%a9%e3%83%ab%e3%82%b3%e3%82%b7%e3%83%b3%e8%aa%98%e5%b0%8e%e4%bd%93-2\/\"> <span class=\"screen-reader-text\">\u9006\u4f59\u5f26\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-383","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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