{"id":30,"date":"2023-09-17T11:02:59","date_gmt":"2023-09-17T11:02:59","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%b5%e3%82%a4%e3%83%b3%e3%81%8b%e3%82%89%e5%b0%8e%e5%87%ba%e3%81%95%e3%82%8c%e3%81%be%e3%81%99\/"},"modified":"2023-09-17T11:02:59","modified_gmt":"2023-09-17T11:02:59","slug":"%e3%82%b3%e3%82%b5%e3%82%a4%e3%83%b3%e3%81%8b%e3%82%89%e5%b0%8e%e5%87%ba%e3%81%95%e3%82%8c%e3%81%be%e3%81%99","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%82%b3%e3%82%b5%e3%82%a4%e3%83%b3%e3%81%8b%e3%82%89%e5%b0%8e%e5%87%ba%e3%81%95%e3%82%8c%e3%81%be%e3%81%99\/","title":{"rendered":"\u30b3\u30b5\u30a4\u30f3\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\uff08\u516c\u5f0f\uff09\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3059\u3002\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u3001\u6bb5\u968e\u7684\u306a\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u5f0f\u306e\u8a3c\u660e\u3001\u30b3\u30b5\u30a4\u30f3\u306e\u4e8c\u6b21\u5c0e\u95a2\u6570\u3001\u3055\u3089\u306b\u306f\u9006\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u3082\u793a\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-coseno\"><\/span>\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306f\u3001\u7b26\u53f7\u5909\u66f4\u3055\u308c\u305f\u30b5\u30a4\u30f3\u95a2\u6570\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001x \u306e\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u30b5\u30a4\u30f3\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\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-72551067d650b8d3797bc37497ec609d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"389\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u30b3\u30b5\u30a4\u30f3\u5f15\u6570\u306b\u95a2\u6570\u304c\u3042\u308b\u5834\u5408\u3001\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306f\u3001\u305d\u306e\u95a2\u6570\u306e\u30b5\u30a4\u30f3\u3092\u5f15\u3044\u305f\u5024\u3068\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u639b\u3051\u305f\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-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 2 \u756a\u76ee\u306e\u5f0f\u306f\u6700\u521d\u306e\u5f0f\u3068\u540c\u7b49\u3067\u3059\u304c\u3001\u9023\u9396\u898f\u5247\u3092\u9069\u7528\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-du-cosinus.webp\" alt=\"\u30b3\u30b5\u30a4\u30f3\u5c0e\u95a2\u6570\" class=\"wp-image-1902\" width=\"428\" height=\"292\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-coseno\"><\/span>\u30b3\u30b5\u30a4\u30f3\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30b3\u30b5\u30a4\u30f3\u516c\u5f0f\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u3068\u3053\u308d\u3067\u3001\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u306e\u5c0e\u51fa\u65b9\u6cd5\u306b\u3064\u3044\u3066\u7591\u554f\u304c\u306a\u304f\u306a\u308b\u3088\u3046\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\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-del-coseno-de-2x\"><\/span>\u4f8b 1: 2x \u306e\u30b3\u30b5\u30a4\u30f3\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-87c696135df266b2d8498b353bf03c36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u30b3\u30b5\u30a4\u30f3\u5f15\u6570\u306b\u306f\u5358\u4e00\u306e x \u306f\u306a\u304f\u3001\u3088\u308a\u8907\u96d1\u306a\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u30b3\u30b5\u30a4\u30f3\u3092\u5c0e\u51fa\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> 2x \u306e\u5c0e\u95a2\u6570\u306f 2 \u3067\u3042\u308b\u305f\u3081\u30012x \u306e\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306f\u30012x \u306e\u30b5\u30a4\u30f3\u3092 2 \u500d\u3057\u305f\u5024\u3092\u5f15\u3044\u305f\u3082\u306e\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-ba75c906f1694fe3fbd16fa61e0d288e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(2x)\\cdot 2=-2\\text{sen}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"532\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-coseno-de-x-al-cuadrado\"><\/span>\u4f8b 2: x \u306e 2 \u4e57\u306e\u4f59\u5f26\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89f1a1fc3f2d5e95aafbd2a37282f88c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"113\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u524d\u306e\u4f8b\u3068\u540c\u69d8\u306b\u3001\u30b3\u30b5\u30a4\u30f3\u5f15\u6570\u306b\u306f x \u3068\u306f\u7570\u306a\u308b\u95a2\u6570\u304c\u3042\u308b\u305f\u3081\u3001\u9023\u9396\u898f\u5247\u3092\u4f7f\u7528\u3057\u3066\u30b3\u30b5\u30a4\u30f3\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-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001x <sup>2<\/sup>\u306e\u5c0e\u95a2\u6570\u306f 2x \u3068\u306a\u308b\u305f\u3081\u3001x \u306e\u30b3\u30b5\u30a4\u30f3\u306e 2 \u4e57\u306e\u5c0e\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a410f3316194c86b97a987b0ec7e9e6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"437\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-coseno-al-cubo\"><\/span>\u4f8b 3: 3 \u4e57\u30b3\u30b5\u30a4\u30f3\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-dfa2e76d23ef3aeb2ab3ff8e20e2aa07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}^3(2x^6-5x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"178\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u306e\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u306f\u5225\u306e\u95a2\u6570\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u5c0e\u95a2\u6570\u3092\u89e3\u304f\u306b\u306f\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-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5f0f\u3092\u9069\u7528\u3059\u308b\u3068\u3001\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u304c\u5f97\u3089\u308c\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-73284bcfb1d5647b2304e323e7fbaedf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=3\\text{cos}^2(2x^6-5x^3)\\cdot \\bigl(-\\text{sen}(2x^6-5x^3)\\bigr)\\cdot (12x^5-15x^2)\\\\[2ex]&amp;=-3\\text{cos}^2(2x^6-5x^3)\\cdot \\text{sen}(2x^6-5x^3)\\cdot (12x^5-15x^2)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"467\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><u style=\"text-decoration-color:#ff951b;\">\u3053\u306e\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u306b\u306f\u3001<\/u> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u96fb\u529b\u30db\u309a\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u306e\u5c0e\u95a2\u6570\/\">\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e<\/a><\/span>\u516c\u5f0f\u3082\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"segunda-derivada-del-coseno\"><\/span>\u30b3\u30b5\u30a4\u30f3\u306e\u4e8c\u6b21\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306b\u3001\u4e09\u89d2\u95a2\u6570\u306e\u6027\u8cea\u306b\u3088\u308a\u3001sin \u306e 2 \u968e\u5fae\u5206\u304c\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3053\u3068\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><u style=\"text-decoration-color:#ff951b;\"><strong>\u6ce8:<\/strong>\u4ee5\u4e0b\u306e\u5185\u5bb9\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\u3001<\/u> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u6d1e\u8a98\u5c0e\u4f53\/\">sine \u306e\u5c0e\u95a2\u6570\u304c\u4f55\u3067\u3042\u308b\u304b<\/a><\/span>\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p> <strong>x \u306e\u30b3\u30b5\u30a4\u30f3\u306e 2 \u968e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u30b3\u30b5\u30a4\u30f3\u3092\u5f15\u3044\u305f\u3082\u306e\u3067\u3059\u3002<\/strong>\u5947\u5999\u306b\u601d\u308f\u308c\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u6570\u5b66\u7684\u306b\u306f\u305d\u306e\u3088\u3046\u3067\u3059\u3002\u5b9f\u969b\u3001\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306f\u30b3\u30b5\u30a4\u30f3\u306a\u306e\u3067\u3001x \u306e\u30b3\u30b5\u30a4\u30f3\u3092 2 \u56de\u5fae\u5206\u3059\u308b\u3068\u3001\u7b26\u53f7\u304c\u5909\u66f4\u3055\u308c\u305f\u30b3\u30b5\u30a4\u30f3\u304c\u518d\u3073\u5f97\u3089\u308c\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-d0d9dda8a4031c367120b1f950da4391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cos}(x)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=-\\text{sen}(x)\\\\[2ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{cos}(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"157\" width=\"132\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u3001\u30b3\u30b5\u30a4\u30f3\u5f15\u6570\u304c x \u3067\u306a\u3044\u5834\u5408\u306b\u5909\u5316\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u9023\u9396\u30eb\u30fc\u30eb\u306e\u9805\u3092\u30c9\u30e9\u30c3\u30b0\u3059\u308b\u305f\u3081\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-83d86bd6508f06b0723153b3b9254c1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cos}(u)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=-\\text{sen}(u)\\cdot u' \\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{cos}(u)\\cdot u'^2 -\\text{sen}(u)\\cdot u'' \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"153\" width=\"263\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-del-coseno-inverso\"><\/span>\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3059\u3079\u3066\u306e\u4e09\u89d2\u95a2\u6570\u306b\u306f\u9006\u95a2\u6570\u304c\u3042\u308a\u3001\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u3082\u9006\u95a2\u6570\u306b\u306a\u308a\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u9006\u4f59\u5f26\u306f\u5fae\u5206\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<p>\u95a2\u6570<strong>\u306e\u9006\u4f59\u5f26\u306e\u5fae\u5206\u5024<\/strong>\u306f\u3001\u95a2\u6570\u306e\u5fae\u5206\u5024\u3092 1 \u306e\u5e73\u65b9\u6839\u3067\u5272\u3063\u305f\u5024\u304b\u3089\u3001\u95a2\u6570\u306e 2 \u4e57\u3092\u5f15\u3044\u305f\u5024\u3092\u5f15\u3044\u305f\u3082\u306e\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-307f91156ee9c404e9c1a1c0de56b102_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}^{-1}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"425\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u9006\u4f59\u5f26\u306f\u9006\u4f59\u5f26\u3068\u3082\u547c\u3070\u308c\u308b\u3053\u3068\u3092\u899a\u3048\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u305f\u3068\u3048\u3070\u30013x \u306e\u9006\u4f59\u5f26\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-7ce426dcd95d21e43b182ef593520c16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}^{-1}(3x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{3}{\\sqrt{1-(3x)^2}}=-\\cfrac{3}{\\sqrt{1-9x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"571\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-coseno\"><\/span>\u30b3\u30b5\u30a4\u30f3\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\u30b3\u30b5\u30a4\u30f3\u95a2\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-c1caebbb3b9acfa8cd25721299f9a22e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{cos}(4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" 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-a89d6e415addae7423aa75362416686b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\text{cos}(2x^3-5x+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"218\" 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-dad34285ad7ac07f34ef408c65cbb96c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f(x)=9\\text{cos}\\left(\\frac{x}{3}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"152\" 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-752bff297c20cdf69d6fcb45290be935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{cos}^5(x^2+3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"187\" 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-939dee8bcafba3f55812c5a13f27a309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\text{cos}\\left(e^{5x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"148\" 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-f6c7c3c5786d010b99f4e65b692dfe1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } \\displaystyle f(x)=9\\text{cos}\\left(\\frac{e^x}{5x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"164\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a3e1b1b2fe486d1c432a075c0028b62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=-\\text{sen}(4x)\\cdot 4 =-4\\text{sen}(4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"285\" 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-8bc2f2e1676bb5f0d4ca231bd35b2b12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=-\\text{sen}(2x^3-5x+1)\\cdot (6x^2-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"321\" 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-cc5cf86d30b34d4cd1a794a4d2ee6a5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f'(x)=-9\\text{sen}\\left(\\frac{x}{3}\\right)\\cdot \\frac{1}{3} =-3\\text{sen}\\left(\\frac{x}{3}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"306\" 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-f168f2e897b18c662f567a25ff09e881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=-5\\text{cos}^4(x^2+3x)\\cdot \\text{sen}(x^2+3x)\\cdot (2x+3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"401\" 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-fe49736d7a1ce1736679e8c25bc4a66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=-\\text{sen}\\left(e^{5x}\\right)\\cdot e^{5x}\\cdot 5=-5\\text{sen}\\left(e^{5x}\\right)\\cdot e^{5x}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"377\" 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-9f4645fb77435daec6f696cffbd54884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{F) }\\displaystyle f'(x)&amp;=-9\\text{sen}\\left(\\frac{e^x}{5x}\\right)\\cdot \\frac{e^x\\cdot 5x-e^x\\cdot 5}{(5x)^2}\\\\[2ex]&amp;=-9\\text{sen}\\left(\\frac{e^x}{5x}\\right)\\cdot \\frac{5e^x(x-1)}{25x^2}\\\\[2ex]&amp;=-9\\text{sen}\\left(\\frac{e^x}{5x}\\right)\\cdot \\frac{e^x(x-1)}{5x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"172\" width=\"310\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-derivada-del-coseno\"><\/span>\u30b3\u30b5\u30a4\u30f3\u5c0e\u95a2\u6570\u306e\u8a3c\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001x \u306e\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u6570\u5b66\u7684\u306b\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u6b21\u306e\u5236\u9650\u306b\u5bfe\u5fdc\u3059\u308b\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-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>\u30b3\u30b5\u30a4\u30f3\u3092\u8a3c\u660e\u3059\u308b\u306e\u3067\u3001\u95a2\u6570\u306f cos(x) \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-a00c11698e4b4f5caf0f227e18be8656_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{cos}(x+h)-\\text{cos}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"245\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5236\u9650\u3092\u4ee3\u5165\u306b\u3088\u3063\u3066\u89e3\u6c7a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u6700\u7d42\u7684\u306b\u306f\u4e0d\u78ba\u5b9a\u306b\u306a\u3063\u3066\u3057\u307e\u3046\u304b\u3089\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u6b21\u306e\u4e09\u89d2\u95a2\u6570\u6052\u7b49\u5f0f\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u5225\u306e\u65b9\u6cd5\u3067\u548c\u306e\u30b3\u30b5\u30a4\u30f3\u3092\u8868\u3059\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-5e06f1728cce31fb5650ba149b8e5b9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cos}(a+b)=\\text{cos}(a)\\text{cos}(b)-\\text{sen}(a)\\text{sen}(b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"307\" 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-db64449e24b11a613417ebce4c7c7a85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{cos}(x)\\text{cos}(h)-\\text{sen}(x)\\text{sen}(h)-\\text{cos}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"380\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u5206\u6570\u3092 2 \u3064\u306e\u5206\u6570\u306b\u5206\u96e2\u3057\u3001\u30b3\u30b5\u30a4\u30f3\u306e\u5171\u901a\u56e0\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-c7c1cd89cf290b01d7d72fc8084f6529_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\left[\\frac{\\text{cos}(x)\\bigl(\\text{cos}(h)-1\\bigr)}{h}-\\frac{\\text{sen}(x)\\text{sen}(h)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"380\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u6e1b\u7b97\u306e\u9650\u754c\u306f\u9650\u754c\u306e\u6e1b\u7b97\u3068\u540c\u3058\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-739fc9a2280c7da1bf2ea830ee5ec88c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{cos}(x)\\bigl(\\text{cos}(h)-1\\bigr)}{h}-\\lim_{h \\to 0}\\frac{\\text{sen}(x)\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"393\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> x \u306e\u30b3\u30b5\u30a4\u30f3\u3068 x \u306e\u30b5\u30a4\u30f3\u306f h \u306b\u4f9d\u5b58\u3057\u306a\u3044\u305f\u3081\u3001\u7bc4\u56f2\u5916\u306b\u62bd\u51fa\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-bfbc83e5a84d91a0f6d98418a4f0041c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{cos}(x)\\lim_{h \\to 0}\\frac{\\text{cos}(h)-1}{h}-\\text{sen}(x)\\lim_{h \\to 0}\\frac{\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"383\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u7121\u9650\u5c0f\u7b49\u4fa1\u7269\u306b\u3088\u308b\u9650\u754c\u306e\u8a08\u7b97\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u6700\u521d\u306e\u9650\u754c\u306f 0\u30012 \u756a\u76ee\u306e\u9650\u754c\u306f 1 \u3067\u3042\u308b\u3068\u7d50\u8ad6\u4ed8\u3051\u3089\u308c\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-f0c2ed1188b80356d05d6188fab5ca47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{cos}(x)\\cdot 0-\\text{sen}(x)\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"223\" 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-9f33ae6c9b18e01ba654772f22cab6d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=-\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306b\u3059\u3067\u306b\u9054\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u7b49\u3057\u3044\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\uff08\u516c\u5f0f\uff09\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3059\u3002\u30b3\u30b5\u30a4\u30f3\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u3001\u6bb5\u968e\u7684\u306a\u6f14\u7fd2\u3067\u7df4\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u5f0f\u306e\u8a3c\u660e\u3001\u30b3\u30b5\u30a4\u30f3\u306e\u4e8c\u6b21\u5c0e\u95a2\u6570\u3001\u3055\u3089\u306b\u306f\u9006\u30b3\u30b5\u30a4\u30f3\u306e\u5c0e\u95a2\u6570\u3082\u793a\u3057\u307e\u3059\u3002 \u30b3\u30b5\u30a4\u30f3\u306e\u5c0e 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