{"id":379,"date":"2023-07-03T19:47:19","date_gmt":"2023-07-03T19:47:19","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%83%a9%e3%82%b8%e3%82%ab%e3%83%ab%e7%84%a1%e7%90%86%e6%a0%b9%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-07-03T19:47:19","modified_gmt":"2023-07-03T19:47:19","slug":"%e3%83%a9%e3%82%b8%e3%82%ab%e3%83%ab%e7%84%a1%e7%90%86%e6%a0%b9%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%83%a9%e3%82%b8%e3%82%ab%e3%83%ab%e7%84%a1%e7%90%86%e6%a0%b9%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u6839\u304b\u3089\u6d3e\u751f"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u30eb\u30fc\u30c8\uff08\u6839\u95a2\u6570\uff09\u306e\u5c0e\u95a2\u6570\u306e\u53d6\u308a\u65b9\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u30eb\u30fc\u30c8\u3092\u5206\u5272\u3059\u308b\u305f\u3081\u306e\u516c\u5f0f\u3068\u3001\u30eb\u30fc\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3059\u308b\u7df4\u7fd2\u554f\u984c\u304c\u898b\u3064\u304b\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-raiz\"><\/span>\u30eb\u30fc\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6839\u306e\u5c0e\u95a2\u6570\u3001<\/strong>\u307e\u305f\u306f\u7121\u7406\u95a2\u6570\u306f\u3001\u6839\u306e\u6307\u6570\u3068\u540c\u3058\u6839\u306e\u7a4d\u3067\u5272\u3063\u305f\u57fa\u6570\u306e\u5c0e\u95a2\u6570 (\u6839\u53f7\u306e\u4e0b\u306e\u5f0f) \u3092\u5272\u308a\u3001\u57fa\u6570\u306e\u6307\u6570\u304b\u3089 1 \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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u305f\u3060\u3057\u3001\u30eb\u30fc\u30c8\u30e9\u30b8\u30ab\u30f3\u30c9\u304c\u5358\u306a\u308b x \u306e\u5834\u5408\u3001\u5f0f\u306f\u7c21\u7d20\u5316\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001x \u306e\u6839\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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u3064\u307e\u308a\u3001\u6839\u3092\u6c42\u3081\u308b\u306b\u306f 2 \u3064\u306e\u516c\u5f0f\u304c\u3042\u308a\u307e\u3059\u30021 \u3064\u76ee\u306f\u5e38\u306b\u4f7f\u7528\u3067\u304d\u30012 \u3064\u76ee\u306f\u57fa\u6570\u304c x \u306e\u5834\u5408\u306b\u306e\u307f\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\/derive-dune-racine.webp\" alt=\"\u6839\u304b\u3089\u6d3e\u751f\u3057\u305f\" class=\"wp-image-1787\" width=\"361\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u3088\u304f\u898b\u308b\u3068\u3001\u5206\u6570\u306e\u5206\u5b50\u306e\u9805\u306f\u3001\u6839\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u3068\u304d\u306b\u9023\u9396\u5f8b\u3092\u9069\u7528\u3057\u305f\u7d50\u679c\u3068\u3057\u3066\u5f97\u3089\u308c\u308b\u9805\u3067\u3059\u3002\u3053\u308c\u304c\u3001\u57fa\u6570\u304c x \u306e\u5834\u5408\u3001x \u306e\u5c0e\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u5206\u6bcd\u306b 1 \u304c\u8868\u793a\u3055\u308c\u308b\u7406\u7531\u3067\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-raices\"><\/span>\u30eb\u30fc\u30c8\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6839\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u8003\u616e\u3057\u3066\u3001\u6839\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u4ee5\u4e0b\u306b\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u8aac\u660e\u3057\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-raiz-cuadrada\"><\/span>\u4f8b 1: \u5e73\u65b9\u6839\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6b21\u306b\u3001\u5e73\u65b9\u6839\u306e\u5c0e\u95a2\u6570\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\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-12533a178fbfb7d1a6b3175d2a812cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u30eb\u30fc\u30c8\u5185\u306e\u5f0f\u306f\u5358\u306a\u308b x \u306a\u306e\u3067\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5e73\u65b9\u6839\u306e\u5c0e\u95a2\u6570\u306f\u30011 \u3092 x \u306e\u5e73\u65b9\u6839\u306e 2 \u500d\u306e\u7a4d\u3067\u5272\u3063\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-5e879d493e8b67755617d2aed1743cde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{2\\sqrt{x^{2-1}}}=\\cfrac{1}{2\\sqrt{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"425\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-raiz-cubica\"><\/span>\u4f8b 2: \u7acb\u65b9\u6839\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-c3c5e7be9bc257eb2866277bae5be644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u30eb\u30fc\u30c8\u306e\u4e0b\u306e\u5f0f\u306f x \u3067\u3042\u308b\u305f\u3081\u3001\u6b21\u306e\u5f0f\u3092\u9069\u7528\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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u7acb\u65b9\u6839\u306e\u5c0e\u95a2\u6570\u306f\u30011 \u3092 x \u306e 2 \u4e57\u306e\u7acb\u65b9\u6839\u306e 3 \u500d\u3067\u5272\u3063\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-f0e928affa231f99c8af7ebffb25049b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{3\\sqrt[3]{x^{3-1}}}=\\cfrac{1}{3\\sqrt[3]{x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"436\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-raiz-cuarta\"><\/span>\u4f8b 3: 4 \u756a\u76ee\u306e\u6839\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-4a02a76ecccf5f654e0a9f7c3fb570e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[4]{7x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73fe\u5728\u3001\u6839\u53f7\u8a18\u53f7\u306e\u4e0b\u306b x \u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u3088\u308a\u8907\u96d1\u306a\u4ee3\u6570\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30eb\u30fc\u30c8\u306e\u5c0e\u95a2\u6570\u306b\u306f\u6b21\u306e\u4e00\u822c\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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u6839\u53f7\u306e\u4e0b\u306e\u5f0f\u306f 1 \u6b21\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u5c0e\u95a2\u6570\u306f 7 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u5168\u4f53\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-d406850e42a532ebe3209ac6d705b0db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[4]{7x-2}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{7}{4\\sqrt[4]{(7x-2)^3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"446\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-4-derivada-de-una-raiz-dentro-de-otra\"><\/span>\u4f8b 4: \u3042\u308b\u30eb\u30fc\u30c8\u304b\u3089\u5225\u306e\u30eb\u30fc\u30c8\u3078\u306e\u6d3e\u751f<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-5955c2ba5e8301beb45ec4fe7207b601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x^2+\\sqrt[3]{x^4-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"180\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5225\u306e\u30eb\u30fc\u30c8\u304b\u3089\u69cb\u6210\u3055\u308c\u308b\u3053\u306e\u30eb\u30fc\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u89e3\u304f\u306b\u306f\u3001\u6b21\u306e\u516c\u5f0f\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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u540c\u3058\u5f0f\u3092\u7d9a\u3051\u3066 2 \u56de\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-c37131b50bda38022296c6401af727ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp; =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot\\left(x^2+\\sqrt[3]{x^4-5}\\right)' \\\\[3ex]&amp;\\displaystyle =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot \\left(2x+\\frac{1}{ 3\\sqrt[3]{(x^4-5)^2}}\\cdot (x^4-5)'\\right)\\\\[3ex]&amp;\\displaystyle =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot \\left(2x+\\frac{1}{ 3\\sqrt[3]{(x^4-5)^2}}\\cdot 4x^3\\right)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"211\" width=\"453\" 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-una-raiz\"><\/span>\u30eb\u30fc\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\u6839\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-3f3ee60a40f0696dc0b5ef1e5bda06ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\sqrt[5]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-e9589007466797e244646623ece04655_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\sqrt[3]{x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"117\" 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-983ef87ac1eca3d1e963de48bb867531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\sqrt{x^2-4x+9}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"189\" 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-24340e19537976608651d3554d8f47b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\sqrt[4]{x^9+5x^4-2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"207\" 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-4f82a43408b63e2399ec88e8a3e2e868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\sqrt[5]{3(x^2-1)^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"181\" 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-5280308e036830e09c0bdcd8bd8791fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\sqrt[6]{x^2+4(5x^3-8x)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"239\" style=\"vertical-align: -6px;\"><\/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-572ec9e7f3b912e18b40787ac9b212b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{1}{5\\sqrt[5]{x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"134\" style=\"vertical-align: -16px;\"><\/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-3bacf51d3e3fd8fa192f982456f2a8d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{4x^3}{3\\sqrt[3]{\\left(x^4\\right)^2}}= \\cfrac{4x^3}{3\\sqrt[3]{x^8}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"225\" style=\"vertical-align: -30px;\"><\/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-3dbbfa5053cc4b46f21eee7a842a00c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=\\cfrac{2x-4}{2\\sqrt{x^2-4x+9}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"204\" style=\"vertical-align: -16px;\"><\/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-5169c93bdfa2522a3219563eee1bb354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=\\cfrac{9x^8+20x^3-2}{4\\sqrt[4]{\\left(x^9+5x^4-2x\\right)^3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"248\" style=\"vertical-align: -30px;\"><\/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-f68dce6e62d98d10d99daf57e0128069_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{3\\cdot 4 \\cdot (x^2-1)^3\\cdot 2x}{5\\sqrt[5]{\\left(3\\left(x^2-1\\right)^4\\right)^4}}=\\cfrac{24x(x^2-1)^3}{5\\sqrt[5]{81\\left(x^2-1\\right)^{16}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"386\" style=\"vertical-align: -41px;\"><\/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-dd1d3bbced66caaed0ac254363e5f2f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{2x+2\\cdot 4(5x^3-8x)\\cdot (15x^2-8)}{6\\sqrt[6]{\\left(x^2+4(5x^3-8x)^2\\right)^5}}=\\cfrac{2x+8(5x^3-8x)(15x^2-8)}{6\\sqrt[6]{\\left(x^2+4(5x^3-8x)^2\\right)^5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"571\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\u30eb\u30fc\u30c8\uff08\u6839\u95a2\u6570\uff09\u306e\u5c0e\u95a2\u6570\u306e\u53d6\u308a\u65b9\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u30eb\u30fc\u30c8\u3092\u5206\u5272\u3059\u308b\u305f\u3081\u306e\u516c\u5f0f\u3068\u3001\u30eb\u30fc\u30c8\u306e\u5c0e\u95a2\u6570\u3092\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3059\u308b\u7df4\u7fd2\u554f\u984c\u304c\u898b\u3064\u304b\u308a\u307e\u3059\u3002 \u30eb\u30fc\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f \u6839\u306e\u5c0e\u95a2\u6570\u3001\u307e\u305f\u306f\u7121\u7406\u95a2\u6570\u306f\u3001\u6839\u306e\u6307\u6570\u3068\u540c\u3058\u6839\u306e\u7a4d\u3067\u5272\u3063 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%83%a9%e3%82%b8%e3%82%ab%e3%83%ab%e7%84%a1%e7%90%86%e6%a0%b9%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u6839\u304b\u3089\u6d3e\u751f<\/span> \u3082\u3063\u3068\u8aad\u3080 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