{"id":28,"date":"2023-09-17T11:03:43","date_gmt":"2023-09-17T11:03:43","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e9%9b%bb%e5%8a%9b%e3%83%9d%e3%83%86%e3%83%b3%e3%82%b7%e3%83%a3%e3%83%ab%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-09-17T11:03:43","modified_gmt":"2023-09-17T11:03:43","slug":"%e9%9b%bb%e5%8a%9b%e3%83%9d%e3%83%86%e3%83%b3%e3%82%b7%e3%83%a3%e3%83%ab%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\/%e9%9b%bb%e5%8a%9b%e3%83%9d%e3%83%86%e3%83%b3%e3%82%b7%e3%83%a3%e3%83%ab%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u3079\u304d\u4e57\uff08\u307e\u305f\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\uff09\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u3079\u304d\u4e57 (\u307e\u305f\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570) \u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u3001\u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3068\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u793a\u3057\u3001\u30b9\u30c6\u30c3\u30d7\u3054\u3068\u306b\u89e3\u3044\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-potencia\"><\/span>\u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u3001\u307e\u305f\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u306f\u3001\u3079\u304d\u4e57\u306e\u6307\u6570\u3068\u5e95\u306e\u7d2f\u4e57\u5024\u304b\u3089\u5e95\u306e\u5c0e\u95a2\u6570\u306e 1 \u500d\u3092\u5f15\u3044\u305f\u7a4d\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5e95\u304c<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6052\u7b49\u95a2\u6570\/\">\u6052\u7b49\u95a2\u6570<\/a><\/span>\u306e\u5834\u5408\u3001\u7d2f\u4e57\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u5358\u7d14\u306b\u95a2\u6570\u306b\u6307\u6570\u3092\u4e57\u7b97\u3057\u3001\u6307\u6570\u304b\u3089 1 \u5358\u4f4d\u3092\u6e1b\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-46eb5b8a4c6968ca5e37af417fd2fb31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5b9f\u969b\u3001\u6052\u7b49\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f 1 \u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u8981\u7d04\u3059\u308b\u3068\u3001\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u3092\u5c0e\u51fa\u3059\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\u9069\u7528\u3067\u304d\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-dune-puissance.webp\" alt=\"\u529b\u304b\u3089\u6d3e\u751f\u3057\u305f\" class=\"wp-image-1760\" width=\"354\" height=\"264\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u3068\u3057\u3066\u63d0\u793a\u3055\u308c\u305f\u6700\u521d\u306e\u5f0f\u304c 2 \u756a\u76ee\u306e\u5f0f\u3068\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u9023\u9396\u5247\u304c\u9069\u7528\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u7c21\u5358\u306b\u691c\u8a3c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u306e\u5f0f\u306f\u3001\u5909\u6570\u304c\u3079\u304d\u4e57\u306e\u5e95\u3067\u3042\u308b\u5834\u5408\u306b\u306e\u307f\u4f7f\u7528\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002x \u304c\u5206\u6bcd\u306b\u3042\u308b\u5834\u5408\u306f\u3001\u6307\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6307\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570\/\">\u6307\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-potencias\"><\/span>\u96fb\u529b\u30c7\u30ea\u30d0\u30c6\u30a3\u30d6\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u7406\u89e3\u3057\u305f\u3089\u3001\u3079\u304d\u4e57\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u304b\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u3001\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-potencia-de-base-x\"><\/span>\u4f8b 1: \u57fa\u6e96\u96fb\u529b x \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-1a77d84e8f9a9d165a989ae8edd67a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u8aac\u660e\u3057\u305f\u3088\u3046\u306b\u3001\u3079\u304d\u4e57\u306e\u5e95\u304c x \u306e\u307f\u306e\u5834\u5408\u3001\u95a2\u6570\u3092\u5c0e\u51fa\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u516c\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46eb5b8a4c6968ca5e37af417fd2fb31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001x \u306e 4 \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-b4f99a41ebf24ffb9dc9d375925fbb03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=4\\cdot x^{4-1}=4x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-potencia-con-parentesis\"><\/span>\u4f8b 2: \u62ec\u5f27\u4ed8\u304d\u306e\u3079\u304d\u4e57\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-c7e7bcf1cc01f1609b200eb0707450f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(2x-1)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u57fa\u6570\u306f\u6052\u7b49\u95a2\u6570\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u306b\u306f\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u62ec\u5f27\u5185\u306e\u95a2\u6570\u306f\u7dda\u5f62\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u5c0e\u95a2\u6570\u306f 2 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\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-8b3fb5d76dac22c3fad5ebe3a0cae630_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(2x-1)^5 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=5\\cdot (2x-1)^4\\cdot 2=10(2x-1)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"577\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-potencia-negativa\"><\/span>\u4f8b 3: \u8ca0\u306e\u3079\u304d\u4e57\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-0bb49a61d47e399ec84ffddce840b4a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(\\log 9x)^{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u6307\u6570\u304c\u8ca0\u3067\u5e95\u304c\u5bfe\u6570\u3067\u3042\u308b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u304c\u3042\u308b\u305f\u3081\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u95a2\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3079\u304d\u6307\u6570\u304c\u8ca0\u306e\u5834\u5408\u3067\u3082\u3001\u305d\u3053\u304b\u3089 1 \u3092\u6e1b\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\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-b883e28fe86b43bae53225fbfc0989c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-2\\cdot (\\log 9x)^{-3}\\cdot \\cfrac{1}{9x\\cdot \\ln 10}\\cdot 9 =\\cfrac{-2(\\log 9x)^{-3}}{x\\ln 10}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"412\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u89e3\u6c7a\u7b56\u306b\u3064\u3044\u3066\u7591\u554f\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u3053\u3053\u3067\u5bfe\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u5bfe\u6570\u95a2\u6570\u30cd\u30d8\u309a\u30ea\u30a2\u30f3\u81ea\u7136\u5bfe\u6570\u306e\u5c0e\u95a2\u6570\/\">\u5bfe\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-4-derivada-de-una-potencia-con-raiz\"><\/span>\u4f8b 4: \u30eb\u30fc\u30c8\u3092\u4f7f\u7528\u3057\u305f\u7d2f\u4e57\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-74c457eaa374d11591afb05c08c79a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{(5x+2)^7}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"149\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u306e\u95a2\u6570\u306f\u3001\u6b63\u898f\u8868\u73fe\u5185\u306e\u7d2f\u4e57\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u6839\u53f7\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u5f0f\u306b\u5909\u63db\u3067\u304d\u308b\u305f\u3081\u3001\u5c0f\u6570\u6307\u6570\u3092\u542b\u3080\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u95a2\u6570\u3092\u7c21\u7565\u5316\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-a851a10c275664fd40272c3f18ebb696_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(5x+2)^{\\frac{7}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u5909\u6570\u306e\u7d2f\u4e57\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u9069\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u5c0e\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-48032a3f39b346214870d2930c0e070f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{7}{3}\\cdot (5x+2)^{\\frac{7}{3}-1} \\cdot 5=\\cfrac{35}{3}(5x+2)^{\\frac{4}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"314\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u30eb\u30fc\u30c8\u5c0e\u95a2\u6570\u30eb\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u3001\u3053\u308c\u3089\u306e\u30bf\u30a4\u30d7\u306e\u95a2\u6570\u3092\u533a\u5225\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u30e9\u30b7\u3099\u30ab\u30eb\u7121\u7406\u6839\u95a2\u6570\u306e\u5c0e\u95a2\u6570\/\">\u30eb\u30fc\u30c8\u304b\u3089\u306e\u6d3e\u751f<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-una-potencia\"><\/span>\u3079\u304d\u4e57\u306e\u5fae\u5206\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u7d2f\u4e57\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-8439a4f480db3b28403219b3d6c617c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"101\" 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-586b1cce6da03d26fc251a34f15b8713_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=3x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"110\" 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-2048513ae93bb32ac7333db56114f8f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=-2x^{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" 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-61b9db052aa145257ef92ac543621b69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=(3x^2-4x)^6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" 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-234c4c2a85b56e062d186e33461534c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=6(x^2+10)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"170\" 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-888598e68e596f15e1e4b585c2287c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\cfrac{1}{(9x+2)^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"156\" 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-bc2353357a484e175ac77e99e4446cb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G) } f(x)=\\sqrt{4x^5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" 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-3e21d4a7733a95b407d4a53114146489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H) } \\displaystyle f(x)=\\left(x^2-4x+\\frac{1}{3}\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"210\" 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-c04e44f3e248cec297f4476885e22a25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I) } f(x)=\\text{sen}^3(6-2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"172\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32e3eaeb51430921053c75da627cacd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=8x^7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"115\" 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-44e8de4cfb9cb267005e390e06c393e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=15x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" 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-4394259c55b711c8668f4d72e3bd4766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=8x^{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"125\" 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-8a916b5238f094595e63d04a86303a7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=6(3x^2-4x)^5\\cdot (3x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" 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-698c94329d2e6edc002bf2b99d4de74e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=3\\cdot 6(x^2+10)^2 \\cdot 2x=36x(x^2+10)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"358\" 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-b2c94d0e23facd72c3a85241bfc4552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=-3\\cdot (9x+2)^{-4}\\cdot 9 =-27(9x+2)^{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"363\" 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-9f488aced09f0e560280f5ce55a1b002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G) } f'(x)=\\cfrac{5}{2}\\cdot 2x^{\\frac{5}{2}-1} =5x^{\\frac{3}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"211\" 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-19d1d31c8415cb654940148ec1a25835_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H) } \\displaystyle f'(x)=4\\left(x^2-4x+\\cfrac{1}{3}\\right)^3\\cdot (2x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"303\" style=\"vertical-align: -23px;\"><\/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-aa9c91854971313e88fde0d535c5a6c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I) } f'(x)=3\\text{sen}^2(6-2x)\\cdot \\text{cos}(6-2x)\\cdot (-2)=-6x\\cdot \\text{sen}^2(6-2x)\\cdot \\text{cos}(6-2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"599\" style=\"vertical-align: -5px;\"><\/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\u3001\u3079\u304d\u4e57 (\u307e\u305f\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570) \u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u3001\u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3068\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u793a\u3057\u3001\u30b9\u30c6\u30c3\u30d7\u3054\u3068\u306b\u89e3\u3044\u305f\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 \u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f \u3079\u304d\u4e57\u306e\u5c0e\u95a2\u6570\u3001\u307e\u305f\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e9%9b%bb%e5%8a%9b%e3%83%9d%e3%83%86%e3%83%b3%e3%82%b7%e3%83%a3%e3%83%ab%e9%96%a2%e6%95%b0%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u3079\u304d\u4e57\uff08\u307e\u305f\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\uff09\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-28","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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