{"id":37,"date":"2023-09-17T11:00:07","date_gmt":"2023-09-17T11:00:07","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e6%b4%be%e7%94%9f%e3%83%ab%e3%83%bc%e3%83%ab%e3%83%81%e3%82%a7%e3%83%bc%e3%83%b3\/"},"modified":"2023-09-17T11:00:07","modified_gmt":"2023-09-17T11:00:07","slug":"%e6%b4%be%e7%94%9f%e3%83%ab%e3%83%bc%e3%83%ab%e3%83%81%e3%82%a7%e3%83%bc%e3%83%b3","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e6%b4%be%e7%94%9f%e3%83%ab%e3%83%bc%e3%83%ab%e3%83%81%e3%82%a7%e3%83%bc%e3%83%b3\/","title":{"rendered":"\u9023\u9396\u30eb\u30fc\u30eb\uff08\u5c0e\u95a2\u6570\uff09"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3068\u306f\u4f55\u304b\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u95a2\u6570\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u89e3\u304b\u308c\u305f\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3057\u3066\u5c0e\u95a2\u6570\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\u6f14\u7fd2\u3092\u884c\u3046\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-regla-de-la-cadena\"><\/span>\u9023\u9396\u306e\u6cd5\u5247\u3068\u306f\u4f55\u3067\u3059\u304b\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u9023\u9396\u5f8b\u306f\u3001\u8907\u5408\u95a2\u6570\u3092\u5c0e\u51fa\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u516c\u5f0f\u3067\u3059\u3002<\/strong>\u9023\u9396\u5247\u3067\u306f\u3001\u8907\u5408\u95a2\u6570<em>f(g(x))<\/em>\u306e\u5fae\u5206\u5024\u306f\u3001\u5fae\u5206\u5024<em>f'(g(x))<\/em>\u306b\u5fae\u5206\u5024<em>g'(x)<\/em>\u3092\u4e57\u7b97\u3057\u305f\u3082\u306e\u306b\u7b49\u3057\u3044\u3068\u898f\u5b9a\u3055\u308c\u3066\u3044\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\/regle-de-la-chaine.webp\" alt=\"\u9023\u9396\u6cd5\u5247\" class=\"wp-image-2207\" width=\"269\" height=\"269\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u95a2\u6570\u306e\u5408\u6210-\u8907\u5408\u95a2\u6570\/\">\u8907\u5408\u95a2\u6570<\/a><\/span><\/p>\n<p>\u975e\u516c\u5f0f\u306b\u306f\u3001\u9023\u9396\u898f\u5247<em>\u3068\u306f\u3001\u95a2\u6570\u3092\u5fae\u5206\u3057\u3001\u305d\u306e\u95a2\u6570\u306b\u542b\u307e\u308c\u308b\u3082\u306e\u3092\u639b\u3051\u308b\u3053\u3068<\/em>\u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u9023\u9396\u5247\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u8907\u5408\u95a2\u6570\u3092\u306f\u308b\u304b\u306b\u7c21\u5358\u306b\u5fae\u5206\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u306e\u5236\u9650\u3092\u4f7f\u7528\u3057\u3066\u95a2\u6570\u306e\u5408\u6210\u3092\u5fae\u5206\u3059\u308b\u5834\u5408\u3001\u591a\u304f\u306e\u8a08\u7b97\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3001\u3053\u306e\u30eb\u30fc\u30eb\u306f\u8907\u5408\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u306e\u307f\u4f7f\u7528\u3055\u308c\u3001\u3042\u3089\u3086\u308b\u7a2e\u985e\u306e\u95a2\u6570\u3084\u95a2\u6570\u3092\u4f7f\u7528\u3057\u305f\u6f14\u7b97\u306b\u306f\u4f7f\u7528\u3055\u308c\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u975e\u5e38\u306b\u3088\u304f\u3042\u308b\u9593\u9055\u3044\u306f\u3001\u305d\u308c\u3092\u9593\u9055\u3048\u3066\u3001\u6b21\u306e\u3088\u3046\u306a\u6a5f\u80fd\u88fd\u54c1\u306b\u9023\u9396\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3059\u308b\u3053\u3068\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-de22604d9af306981b71d39bd190df75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x)\\cdot x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"68\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u274c<\/p>\n<p>\u9023\u9396\u30eb\u30fc\u30eb\u306f\u3001<strong>\u3042\u308b\u95a2\u6570\u306e\u4e2d\u306b\u5225\u306e\u95a2\u6570\u304c\u3042\u308b\u5834\u5408\u306b<\/strong>\u306e\u307f\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-ea93fb0bbc6f1ac5c2e26f2c5730627f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"45\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u2705 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-con-la-regla-de-la-cadena\"><\/span>\u9023\u9396\u5f8b\u306b\u3088\u308b\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u9023\u9396\u30eb\u30fc\u30eb\u306e\u5b9a\u7fa9\u3092\u8003\u616e\u3057\u3066\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u4f8b\u3068\u3057\u3066\u3044\u304f\u3064\u304b\u306e\u95a2\u6570\u3092\u5c0e\u304d\u51fa\u3057\u307e\u3059\u3002\u4f8b\u306e\u4e2d\u3067\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u95a2\u6570\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u306e\u304b\u7406\u89e3\u3067\u304d\u306a\u3044\u5834\u5408\u306f\u3001\u30b3\u30e1\u30f3\u30c8\u3067\u8cea\u554f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u4f8b1<\/h3>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u9023\u9396\u5247\u3092\u4f7f\u7528\u3057\u3066 x \u306e 2 \u4e57\u306e\u81ea\u7136\u5bfe\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-056e8e809ecf361f98a9ab4a6509e1a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u81ea\u7136\u5bfe\u6570\u306e\u5c0e\u95a2\u6570\u306f\u305d\u306e\u5f15\u6570\u306e 1 \u500d\u306b\u7b49\u3057\u3044\u305f\u3081\u3001\u5c0e\u95a2\u6570\u306f<\/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-4537be7e40864f78dd4bf5a5cdfb53ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'\\bigl(g(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -7px;\"><\/p>\n<p>\u306a\u308c\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-82f88b45158f1890a0e60b2496a1898e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"331\" style=\"vertical-align: -12px;\"><\/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-b66cdf74d9a89d4259495d799042e18c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\ln(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\cfrac{1}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"396\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4e00\u65b9\u3001x \u306e 2 \u4e57\u5c0e\u95a2\u6570\u306f 2x \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-0f0a7b2d096f09aacc349fe800f5ae6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u5f8c\u306b\u3001\u9023\u9396\u5247\u3092\u9069\u7528\u3057\u3066\u95a2\u6570\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u8907\u5408\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f\u3001\u5148\u307b\u3069\u898b\u3064\u3051\u305f 2 \u3064\u306e\u5c0e\u95a2\u6570\u306e\u7a4d\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-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" 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-6ad6b9a4a227664b616ffeef61781e54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x^2}\\cdot 2x = \\cfrac{2x}{x^2}=\\cfrac{2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"458\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> \u4f8b 2<\/h3>\n<p>\u3053\u306e 2 \u756a\u76ee\u306e\u4f8b\u3067\u306f\u3001\u591a\u9805\u5f0f\u306b\u57fa\u3065\u3044\u3066\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\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-1fd64daeb147f4af91e5eb8518621081_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^2+4x-5\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"179\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u3079\u304d\u4e57\u3092\u5c0e\u51fa\u3059\u308b\u306b\u306f\u3001\u5143\u306e\u6307\u6570\u3092\u305d\u306e\u524d\u306b\u7f6e\u304d\u3001\u6307\u6570\u304b\u3089 1 \u5358\u4f4d\u3092\u6e1b\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3057\u306a\u3044\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\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-9d0e7fc8a11cbd2103465a57128a9db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\left(3x^2+4x-5\\right)^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=3\\left(3x^2+4x-5\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"582\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u62ec\u5f27\u5185\u306b\u3042\u308b\u3082\u306e\u3092\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-dad3522b805cdb0c38e771bc6e630f50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=3x^2+4x-5\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=6x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"424\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u5f8c\u306b\u3001\u9023\u9396\u5247\u3092\u4f7f\u7528\u3057\u3066\u95a2\u6570\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u3092\u89e3\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u524d\u306b\u8a08\u7b97\u3057\u305f 2 \u3064\u306e\u5c0e\u95a2\u6570\u306e\u4e57\u7b97\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-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" 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-4d4d80ad509263a9791efd441621d183_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^2+4x-5\\right)^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=3\\left(3x^2+4x-5\\right)^2\\cdot (6x+4)\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"582\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u4f8b 3<\/h3>\n<p>\u3053\u306e\u5834\u5408\u3001x \u306e 3 \u4e57\u3068 7x \u306e\u6b63\u5f26\u5c0e\u95a2\u6570\u3092\u89e3\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-42b994d7e38385bd61050cc50428beeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3+7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5b9f\u969b\u3001\u3053\u308c\u306f\u95a2\u6570\u306e\u5408\u6210\u3067\u3059\u3002\u30b5\u30a4\u30f3\u95a2\u6570\u5185\u306b\u95a2\u6570 x <sup>3<\/sup> +7x \u304c\u3042\u308b\u305f\u3081\u3001\u9023\u9396\u5247\u3092\u4f7f\u7528\u3057\u3066\u5408\u6210\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3067\u306f\u3001\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306f\u30b3\u30b5\u30a4\u30f3\u3067\u3042\u308b\u305f\u3081\u3001\u5916\u90e8\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f\u30b5\u30a4\u30f3\u3068\u540c\u3058\u5f15\u6570\u3092\u6301\u3064\u30b3\u30b5\u30a4\u30f3\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-e4b784343e9e483f8f3e2bb0cd465335_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}(x^3+7x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\text{cos}(x^3+7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"522\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u4e00\u65b9\u3001x <sup>3<\/sup> +7x \u306e\u5c0e\u95a2\u6570\u306f 3x <sup>2<\/sup> +7 \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-395ee5862baf231657c05660e22bbd42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^3+7x\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=3x^2+7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"392\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u8907\u5408\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f\u3001\u6b21\u306e 2 \u3064\u306e\u5c0e\u95a2\u6570\u306e\u7a4d\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-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" 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-5b44098b23fd39005532d5f42593f585_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3+7x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^3+7x)\\cdot (3x^2+7)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"555\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-con-la-regla-de-la-cadena\"><\/span>\u9023\u9396\u30eb\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u305f\u5c0e\u95a2\u6570\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 1<\/h3>\n<p>\u9023\u9396\u30eb\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u8907\u5408\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-b84ea805fb8c56d493151d0f9b72b628_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(5x^2-6x\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"149\" 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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5916\u90e8\u95a2\u6570\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\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-82e232ad4bd7b0f1b4b93625bd8dcf2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=a\\bigl(g(x)\\bigr)^n \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=n\\cdot a\\bigl(g(x)\\bigr)^{n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"397\" 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-058311927ac43c45c1de7d799d802310_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\left(5x^2-6x\\right)^3\\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= 3\\left(5x^2-6x\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"415\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u3001\u5185\u90e8\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3079\u304d\u4e57\u306e\u6e1b\u7b97\u3067\u3042\u308b\u305f\u3081\u3001\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u5f0f\u3092\u5404\u9805\u306b\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-eda0577ba91756ce6852219b0b1bf4c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=ax^n \\ \\longrightarrow \\ f'(x)=n\\cdot ax^{n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" 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-b4b1fc6c2a94bb4e9833be8140196f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=5x^2-6x\\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1c9d99adf81a8861bbd2dee3b8a7fcee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g'(x)=2\\cdot 5x^1-1 \\cdot 6 x^0 =10x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3064\u307e\u308a\u3001\u8907\u5408\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f\u3001\u6b21\u306e 2 \u3064\u306e\u5c0e\u95a2\u6570\u306e\u7a4d\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-f3e6ffbcb906ced150b00cf463b56434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(5x^2-6x\\right)^3 \\ \\longrightarrow \\ \\bm{f'(x)= 3\\left(5x^2-6x\\right)^2\\cdot (10x-6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 2<\/h3>\n<p>\u9023\u9396\u5247\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u8907\u5408\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u89e3\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-c6ecb2411e5245a58c614748280b4568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-3\\left(5x^5+9x^3\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"182\" 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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u307e\u305a\u3001\u5916\u90e8\u95a2\u6570\u306e\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-2e5d21c7196c7ebaeaf6ca11762ca251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr) &amp; =4 \\cdot ( -3) \\left(5x^5+9x^3\\right)^3 \\\\[1.5ex]&amp;=-12\\left(5x^5+9x^3\\right)^3 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"357\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u4eca\u5ea6\u306f\u5185\u90e8\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u89e3\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-fe839a2f2eb9412f63700dab70bf18f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=5x^5+9x^3\\ \\longrightarrow \\ g'(x)=25x^4+27x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"335\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-0fe8c7e374a30ed8bcf0a83cea68d6bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-3\\left(5x^5+9x^3\\right)^4 \\ \\longrightarrow \\ \\bm{f'(x)=-12\\left(5x^5+9x^3\\right)^3\\cdot \\left(25x^4+27x^2\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"549\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 3<\/h3>\n<p>\u9023\u9396\u5247\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u95a2\u6570\u306e\u69cb\u6210\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-555bcc9c8b61b47c73e2014749954305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{2x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"87\" style=\"vertical-align: -5px;\"><\/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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u6307\u6570\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\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-f52dc9e8ea936ea4de492bb3be18ebb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{x} \\ \\longrightarrow \\ f'(x)=e^{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"204\" 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-02e55bcf16e8288e1729ed5a4d06ed9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=e^{2x^3} \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= e^{2x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"281\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u307e\u305f\u3001\u95a2\u6570\u3068\u95a2\u6570\u306e\u6307\u6570\u3082\u533a\u5225\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-b17b1c7b9b871d8404166d92d5cb0974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=2x^3 \\ \\longrightarrow \\ g'(x)=6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u3001\u9023\u9396\u898f\u5247\u3092\u4f7f\u7528\u3057\u3066\u3001\u6574\u6570\u8907\u5408\u95a2\u6570\u306e\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-ad4635f85ae781dd1565a8f6581d26c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{2x^3} \\ \\longrightarrow \\ \\bm{f'(x)= e^{2x^3}\\cdot 6x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 4<\/h3>\n<p>\u9023\u9396\u5f8b\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u8907\u5408\u95a2\u6570\u306e\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-a10feee3fd85abefa9ec5ea79c0cf223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{\\text{sen}(x) +x }\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" 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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u7121\u7406\u95a2\u6570\u306e\u5f15\u6570\u306b\u6b63\u5f26\u95a2\u6570\u3068\u7dda\u5f62\u95a2\u6570\u304c\u3042\u308b\u306e\u3067\u3001\u3053\u308c\u306f\u95a2\u6570\u306e\u5408\u6210\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306b\u30eb\u30fc\u30c8\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-64a603462f094d4c699c56453463ca49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x} \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"265\" 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-e909efbe50930f94cce0b2485b060046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\sqrt[3]{\\text{sen}(x) +x } \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= \\cfrac{1}{3\\sqrt[3]{\\bigl(\\text{sen}(x) +x\\bigr)^2 }}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"455\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u4eca\u3001\u30e9\u30b8\u30ab\u30eb\u304b\u3089\u8b70\u8ad6\u3092\u5c0e\u304d\u51fa\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u95a2\u6570\u306e\u5408\u8a08\u3067\u3042\u308b\u305f\u3081\u3001\u5c0e\u95a2\u6570\u306f\u5404\u9805\u306e\u5c0e\u95a2\u6570\u306e\u5408\u8a08\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-ffa1d177a8dfe81684225dffd555e6fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=\\text{sen}(x) +x \\ \\longrightarrow \\ g'(x)=\\cos(x) + 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"326\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u306f\u3001\u8a08\u7b97\u3055\u308c\u305f 2 \u3064\u306e\u5c0e\u95a2\u6570\u306e\u4e57\u7b97\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-fad132b49a5faab86a3955efd5422973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f(x)=\\sqrt[3]{\\text{sen}(x)+x} \\ \\longrightarrow \\ f'(x)&amp; = \\cfrac{1}{3\\sqrt[3]{\\bigl(\\text{sen}(x) +x\\bigr)^2 }} \\cdot \\bigl(\\cos(x) + 1 \\bigr)\\\\[1.5ex]&amp;=\\cfrac{\\bm{\\cos(x) + 1}}{\\bm{3\\sqrt[3]{\\bigl(\\mathbf{sen}(x) +x\\bigr)^2} }}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"509\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 5<\/h3>\n<p>\u9023\u9396\u898f\u5247\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u95a2\u6570\u306e\u69cb\u6210\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-09f37b7970003fc0221e15dccc157ccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x^2+5}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"100\" style=\"vertical-align: -5px;\"><\/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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9023\u9396\u5247\u3092\u9069\u7528\u3059\u308b\u306b\u306f\u3001\u3079\u304d\u4e57\u3068\u591a\u9805\u5f0f\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u3001\u305d\u308c\u3089\u3092\u4e57\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5bfe\u5fdc\u3059\u308b\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u96fb\u529b\u3092\u5c0e\u304d\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-a9fb428e4d74e0f972130fde4e48ac0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a^x \\ \\longrightarrow \\ f'(x)=a^x\\cdot \\ln (a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"256\" 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-b1d18c3443d6398dcefba063ac556cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=3^{x^2+5} \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= 3^{x^2+5}\\cdot  \\ln(3)\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"355\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u6307\u6570\u304b\u3089\u591a\u9805\u5f0f\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-6070c83f8944ee39ae4e3e6e125bcc72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2+5 \\ \\longrightarrow \\ g'(x)=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"235\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u9023\u9396\u5f8b\u306f\u3001\u95a2\u6570\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u304c\u3001\u4eca\u898b\u3064\u3051\u305f\u5c0e\u95a2\u6570\u306e\u7a4d\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-bc0c78749a089e832984e3844345b6f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x^2+5} \\ \\longrightarrow \\ \\bm{f'(x)= 3^{x^2+5}\\cdot  \\ln(3) \\cdot 2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"337\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 6 <\/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-6c85e9125bf4f54041c798dc4cc8975d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln \\bigl(4x^2 \\cdot \\cos(x) \\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"174\" 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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u81ea\u7136\u5bfe\u6570\u306e\u5f15\u6570\u306b\u306f 2 \u3064\u306e\u7570\u306a\u308b\u30bf\u30a4\u30d7\u306e\u95a2\u6570\u306e\u7a4d\u304c\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u554f\u984c\u306e\u95a2\u6570\u306f\u660e\u3089\u304b\u306b\u5408\u6210\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u307e\u305a\u5bfe\u6570\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-a18d7f43ff1861389379485ae00db981_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x) \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"223\" style=\"vertical-align: -12px;\"><\/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-9b6ac8614a0671889738a762d0be9c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\ln \\bigl(4x^2 \\cdot \\cos(x) \\bigr) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= \\cfrac{1}{4x^2 \\cdot \\cos(x) }\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"430\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u5bfe\u6570\u5f15\u6570\u304b\u3089\u95a2\u6570\u3092\u5c0e\u51fa\u3057\u307e\u3059\u3002\u3053\u308c\u306f 2 \u3064\u306e\u95a2\u6570\u306e\u4e57\u7b97\u3067\u3042\u308b\u305f\u3081\u3001\u5c0e\u51fa\u3059\u308b\u306b\u306f\u6b21\u306e\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-cd35f94998c8450bd2e65e92eeecea2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x) \\cdot g(x) \\ \\longrightarrow \\ z'(x)=f'(x)\\cdot g(x)+f(x) \\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"439\" 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-643ddf7ec82cbcc3bc685ceadf59da98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}g(x)=4x^2 \\cdot \\cos(x) \\ \\longrightarrow \\ g'(x) &amp; = 8x\\cdot \\cos(x) + 4x^2 \\cdot \\bigl(- \\text{sen}(x)\\bigr) \\\\[2ex] &amp; = 8x\\cdot \\cos(x) - 4x^2 \\cdot  \\text{sen}(x)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"472\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u306f\u3001\u9023\u9396\u5247\u306b\u5f93\u3063\u3066\u3001\u6b21\u306e 2 \u3064\u306e\u5c0e\u95a2\u6570\u306e\u7a4d\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-6912d0951fb85a61df21cbed282000f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;= \\cfrac{1}{4x^2 \\cdot \\cos(x) } \\cdot \\bigl( 8x\\cdot \\cos(x) - 4x^2 \\cdot  \\text{sen}(x) \\bigr)\\\\[1.5ex]&amp;=\\cfrac{8x\\cdot \\cos(x) - 4x^2 \\cdot\\text{sen}(x)}{4x^2 \\cdot \\cos(x)}\\\\[1.5ex]&amp;=\\cfrac{\\bm{2\\cos(x) - x \\cdot }\\mathbf{sen}\\bm{(x)}}{\\bm{x \\cdot \\cos(x) }}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"169\" width=\"368\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 7<\/h3>\n<p>\u9023\u9396\u5f8b\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u89e3\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-3eb7a0c588b3aac39a2a4aa49a691598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_9 (e^{x^2}-6x^7)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"174\" style=\"vertical-align: -5px;\"><\/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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u308c\u306f\u95a2\u6570\u306e\u5408\u6210\u306a\u306e\u3067\u3001\u5bfe\u6570\u3068\u305d\u306e\u5f15\u6570\u3092\u5225\u3005\u306b\u5fae\u5206\u3057\u3001\u5c0e\u95a2\u6570\u3092\u639b\u3051\u307e\u3059\u3002<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u307e\u305a\u3001\u5bfe\u6570\u3092\u5e95 9 \u3067\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-2c3339cb70e45253b4994a0c740202cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a (x) \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{x\\cdot \\ln (a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"289\" 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-b0b4fc286244d6e5e35b8f7e94961314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\log_9 (e^{x^2}-6x^7) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=\\cfrac{1}{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"479\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u5bfe\u6570\u306e\u5f15\u6570\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u6570\u5024 e \u306e\u5f15\u6570\u306b\u306f\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3064\u307e\u308a\u3001\u305d\u308c\u306f\u8907\u5408\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u95a2\u6570\u3092\u5c0e\u51fa\u3059\u308b\u306b\u306f\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-34065617ade6fb28fe66bc3f57a49cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h(x)=e^{x^2} \\ \\longrightarrow \\ h'(x)=e^{x^2}\\cdot \\bigl(x^2\\bigr)' =e^{x^2}\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"348\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u3057\u305f\u304c\u3063\u3066\u3001\u5bfe\u6570\u306e\u6574\u6570\u5f15\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-1f7cd729a06f3cde16890b587693a667_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)= e^{x^2}-6x^7\\ \\longrightarrow \\ g'(x)=e^{x^2}\\cdot 2x - 42x^6\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"352\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u95a2\u6570\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u306f f'(g(x)) \u3068 g'(x) \u306e\u7a4d\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-2a702df902c9f1eff66e14836a262c0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{1}{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)} \\cdot \\bigl(e^{x^2}\\cdot 2x - 42x^6\\bigr)\\\\[1.5ex]&amp;=\\cfrac{\\bm{e^{x^2}\\cdot 2x - 42x^6}}{\\bm{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"342\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u6f14\u7fd2 8<\/h3>\n<p>\u9023\u9396\u30eb\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u6b21\u306e\u8907\u5408\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-0fa2f9b67e41d5edc5bbef249f598359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"231\" style=\"vertical-align: -17px;\"><\/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\u898b\u308b<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u3053\u306e\u6f14\u7fd2\u3067\u306f\u8907\u6570\u306e\u95a2\u6570\u3092\u69cb\u6210\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u9023\u9396\u30eb\u30fc\u30eb\u3092\u6570\u56de\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305a\u3001\u30b5\u30a4\u30f3\u304b\u3089\u4e09\u89d2\u95a2\u6570\u3092\u5c0e\u51fa\u3057\u307e\u3059\u3002\u305d\u306e\u5c0e\u95a2\u6570\u306f\u30b3\u30b5\u30a4\u30f3\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-b6d04ed6e1b20f210641bb48c25c2c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=\\cos\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"569\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b21\u306b\u3001\u9023\u9396\u5247\u3092\u4f7f\u7528\u3057\u3066\u6b63\u5f26\u5f15\u6570\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-2e1c2492990456e277e493c898cb3924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} g(x)= \\Bigl( 9x^5 + \\cos(x) \\Bigr)^2 \\cdot g'(x) &amp;= 2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(9x^5 + \\cos(x) \\Bigr)' \\\\[1.5ex]&amp;=2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(45x^4-\\text{sen}(x)\\Bigr)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"519\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u5f8c\u306b\u3001\u9023\u9396\u898f\u5247\u3092\u518d\u5ea6\u9069\u7528\u3057\u3066\u3001\u95a2\u6570\u306e\u69cb\u6210\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u3092\u53d6\u5f97\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-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" 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-db5ac3368ea7d37f280e0f538aaed1a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f'(x)=\\cos } \\bm{\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr) \\cdot 2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(45x^4-}\\mathbf{sen}\\bm{(x)\\Bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"510\" style=\"vertical-align: -17px;\"><\/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-regla-de-la-cadena\"><\/span>\u30c1\u30a7\u30fc\u30f3\u30eb\u30fc\u30eb\u306e\u8a3c\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u9023\u9396\u5247\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u5c0e\u95a2\u6570\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u304b\u3089\u59cb\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-dc1699622d128f888c1f20599aeccf60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"219\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> <em>z \u3092<\/em>2 \u3064\u306e\u95a2\u6570\u3067\u69cb\u6210\u3055\u308c\u308b\u95a2\u6570\u3068\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-6a650ba7c58d41f371d90a56e4d4fd4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=f\\bigl(g(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"90\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u5b9a\u7fa9\u3092\u9069\u7528\u3057\u305f\u95a2\u6570<em>z<\/em>\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-9419bc1d5617600c2ffea842822efed7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"269\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u3059\u3067\u306b\u3054\u5b58\u77e5\u306e\u3068\u304a\u308a\u3001\u540c\u3058\u9805\u3067\u5206\u6570\u306e\u4e57\u7b97\u3068\u9664\u7b97\u3092\u884c\u3063\u3066\u3082\u7d50\u679c\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u9032\u3080\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-18ff4ca3bcd8ba04a25aa0187b3b5b3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{h}\\cdot \\frac{g(x+h)-g(x)}{g(x+h)-g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u306e\u5206\u6bcd\u3092\u4e26\u3079\u66ff\u3048\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-9059bbff916941c2e161b6d127ec654e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{g(x+h)-g(x)}\\cdot \\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u9650\u754c\u306e\u7279\u6027\u3092\u9069\u7528\u3059\u308b\u3068\u3001\u4e0a\u8a18\u306e\u9650\u754c\u3092 2 \u3064\u306b\u5206\u5272\u3067\u304d\u307e\u3059\u3002\u7a4d\u306e\u9650\u754c\u306f\u9650\u754c\u306e\u7a4d\u306b\u7b49\u3057\u3044\u305f\u3081\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-220a40fee3825089394f3d6e5578c4eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{g(x+h)-g(x)}\\cdot \\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"436\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001\u3053\u306e\u5f0f\u306f\u6b21\u3068\u540c\u7b49\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-8188c6fac1c61928975e7a8c02ac79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"175\" style=\"vertical-align: 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