{"id":31,"date":"2023-09-17T11:02:40","date_gmt":"2023-09-17T11:02:40","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-09-17T11:02:40","modified_gmt":"2023-09-17T11:02:40","slug":"%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u63a5\u7dda\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u6b63\u63a5\u95a2\u6570\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u304b\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u63a5\u7dda\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u305f\u308a\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\u6f14\u7fd2\u3067\u7df4\u7fd2\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u6b63\u63a5\u5fae\u5206\u516c\u5f0f\u3092\u793a\u3057\u3001\u9006\u6b63\u63a5\u5fae\u5206\u516c\u5f0f\u3082\u793a\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-de-la-tangente\"><\/span>\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>x \u306e\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u30b3\u30b5\u30a4\u30f3\u306e 2 \u4e57\u3067 1 \u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/strong> x \u306e\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306f\u3001x \u306e\u6b63\u5272\u306e 2 \u4e57\u3001\u304a\u3088\u3073 x \u306e\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e 2 \u4e57\u306b 1 \u3092\u52a0\u3048\u305f\u3082\u306e\u3068\u7b49\u4fa1\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-dfb81626a982a908c4e517b1ecb748e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{tan}(x)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=\\cfrac{1}{\\text{cos}^2(x)}=\\text{sec}^2(x)=1+\\text{tan}^2(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"308\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3059\u3079\u3066\u306e\u5f0f\u306f\u540c\u7b49\u3067\u3042\u308b\u305f\u3081\u3001\u6b63\u63a5\u95a2\u6570\u3092\u5c0e\u51fa\u3059\u308b\u53ef\u80fd\u306a\u5f0f\u306f 3 \u3064\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3001\u63a5\u7dda\u5f15\u6570\u306b x \u3068\u306f\u7570\u306a\u308b\u95a2\u6570\u304c\u3042\u308b\u5834\u5408 (\u3053\u308c\u3092 u \u3068\u547c\u3073\u307e\u3059)\u3001\u9023\u9396\u898f\u5247\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001u \u306e\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\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-1ad272ab857ecf57ebc79e68a4370fc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{tan}(u)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}=\\text{sec}^2(u)\\cdot u'=\\left(1+\\text{tan}^2(u)\\right)\\cdot u'\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"380\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3064\u307e\u308a\u3001\u63a5\u7dda\u5c0e\u95a2\u6570\u30eb\u30fc\u30eb\u306f\u6b21\u306e\u3088\u3046\u306b\u8981\u7d04\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-de-la-tangente.webp\" alt=\"\u63a5\u7dda\u5c0e\u95a2\u6570\" class=\"wp-image-1929\" width=\"418\" height=\"365\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-tangente\"><\/span>\u63a5\u7dda\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u63a5\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u8003\u616e\u3057\u3066\u3001\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u6b63\u63a5\u95a2\u6570\u306e\u5c0e\u51fa\u65b9\u6cd5\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u5c0e\u95a2\u6570\u306e\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u89e3\u304d\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-tangente-de-2x\"><\/span>\u4f8b 1: 2x \u306e\u6b63\u63a5\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-f238988096540344626a3079f65a0753_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u4e0a\u3067\u898b\u305f 3 \u3064\u306e\u516c\u5f0f\u306e\u3044\u305a\u308c\u304b\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u30b3\u30b5\u30a4\u30f3\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-47c1f81edd8b591f33ab986d4de73a34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u95a2\u6570 2x \u306f\u7dda\u5f62\u306a\u306e\u3067\u3001\u5c0e\u95a2\u6570\u306f 2 \u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012x \u306e\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306f 2x \u306e\u30b3\u30b5\u30a4\u30f3\u306e 2 \u4e57\u3067 2 \u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e18c22b2cabb93a6081363bc618840b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{\\text{cos}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-tangente-de-x-al-cuadrado\"><\/span>\u4f8b 2: x \u306e 2 \u4e57\u306e\u6b63\u63a5\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-9c6defebe72239c5288ece20976d9a50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6b63\u63a5\u5f15\u6570\u95a2\u6570\u306f x \u3067\u306f\u306a\u304f\u3001\u5c0e\u95a2\u6570\u3092\u6301\u3064\u95a2\u6570\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u305d\u308c\u3092\u5c0e\u51fa\u3059\u308b\u306b\u306f\u9023\u9396\u898f\u5247\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-47c1f81edd8b591f33ab986d4de73a34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> x \u306e 2 \u4e57\u306e\u5c0e\u95a2\u6570\u306f 2x \u3067\u3042\u308b\u305f\u3081\u3001x <sup>2<\/sup>\u306e\u6b63\u63a5\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-111ca482f4c688c676c10b2ed80d6567_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{\\text{cos}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"403\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-tangente-al-cubo\"><\/span>\u4f8b 3: \u7acb\u65b9\u4f53\u306e\u63a5\u7dda\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-a70568c32830f1f20ab7a5885bf999ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}^3(9x^2-4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"172\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u554f\u984c\u3067\u306f\u5408\u6210\u95a2\u6570\u304c\u3042\u308b\u305f\u3081\u3001\u63a5\u7dda\u3092\u5fae\u5206\u3059\u308b\u305f\u3081\u306b\u9023\u9396\u898f\u5247\u3082\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-47c1f81edd8b591f33ab986d4de73a34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3055\u3089\u306b\u3001\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306f 3 \u4e57\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5fae\u5206\u306e\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u524d\u306b\u3001\u3079\u304d\u4e57\u306e\u516c\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-424a7372a1d97a5c17a86d6253666164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=3\\text{tan}^2(9x^2-4x)\\cdot \\cfrac{18x-4}{\\text{cos}^2(9x^2-4x)} \\\\[2ex]&amp;=\\cfrac{3\\text{tan}^2(9x^2-4x)\\cdot(18x-4)}{\\text{cos}^2(9x^2-4x)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"110\" width=\"314\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-la-tangente-inversa\"><\/span>\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4ed6\u306e\u9006\u95a2\u6570\u3068\u540c\u69d8\u306b\u3001\u6b63\u63a5\u95a2\u6570\u306b\u306f\u9006\u6b63\u63a5\u95a2\u6570\u3068\u3044\u3046\u9006\u95a2\u6570\u3082\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u5c0e\u51fa\u3059\u308b\u516c\u5f0f\u306f\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u516c\u5f0f\u3068\u306f\u4f3c\u3066\u3044\u307e\u305b\u3093\u304c\u3001\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u5f79\u7acb\u3064\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n<p>\u95a2\u6570<strong>\u306e\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306f<\/strong>\u3001\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092 1 \u3067\u5272\u3063\u305f\u5546\u306b\u3001\u305d\u306e\u95a2\u6570\u306e 2 \u4e57\u3092\u52a0\u3048\u305f\u5546\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-d26f5f19ebcdab218e6d1924e18845f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}^{-1}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"398\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u305f\u3068\u3048\u3070\u30013x \u306e\u9006\u6b63\u63a5\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-bdabf1792179bdd9281695a65dcd0912_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}^{-1}(3x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{3}{1+(3x)^2}=\\cfrac{3}{1+9x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"513\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-la-tangente\"><\/span>\u63a5\u7dda\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\u6b63\u63a5\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-e0c187638a259878b3cf6382751c2718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{tan}(3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" 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-573c097d9cddb7837803e4aceaec362a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\text{tan}(x^3-10x^2+8)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" 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-4e140710c7f1fea51f3fe280f30fdb1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f(x)=\\text{tan}^2\\left(\\frac{x}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"153\" 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-49b86302e59ffb338f425f4e5a97be89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{tan}\\left(e^{2x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"151\" 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-4af042cb47d433a0eeff44d9c5349873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\text{tan}\\bigl(\\ln(4x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"171\" 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-21464f892729c58a42f796e0d35f6a89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{tan}\\left(\\sqrt{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"159\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-240652ca6b9fbabd52d65974bf3e4793_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{3}{\\text{cos}^2(3x)}\" 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-5166bb8a8d3af33cc82165b63e2b6a52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{3x^2-20x}{\\text{cos}^2(x^3-10x^2+8)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"241\" 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-94a4f0132583e89119dae1b25be65adf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f'(x)=2\\text{tan}\\left(\\frac{x}{2}\\right)\\cdot \\frac{1}{\\text{cos}^2\\left(\\frac{x}{2}\\right)}\\cdot \\frac{1}{2}=\\frac{\\text{tan}\\left(\\frac{x}{2}\\right)}{\\text{cos}^2\\left(\\frac{x}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"354\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2d4f13da08be6a975b3e8710f5aee58c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=\\cfrac{2e^{2x}}{\\text{cos}^2(e^{2x})}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"160\" 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-cd7569c56712ac42fa2fe9300d9e4896_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{\\frac{4}{4x}}{\\text{cos}^2\\bigl(\\ln(4x)\\bigr)}=\\cfrac{1}{x\\cdot\\text{cos}^2\\bigl(\\ln(4x)\\bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"329\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a51deebd15244b70a6917a9ea2a456a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{\\frac{3}{2\\sqrt{3x}}}{\\text{cos}^2\\left(\\sqrt{3x}\\right)}=\\cfrac{3}{2\\sqrt{3x}\\cdot \\text{cos}^2\\left(\\sqrt{3x}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -21px;\"><\/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-de-la-tangente\"><\/span>\u63a5\u7dda\u306e\u5c0e\u95a2\u6570\u306e\u8a3c\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u308c\u304c\u67b6\u7a7a\u306e\u5f0f\u3067\u306f\u306a\u3044\u3053\u3068\u3092\u78ba\u8a8d\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u3092\u4f7f\u7528\u3057\u3066\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u30013 \u3064\u306e\u4e09\u89d2\u6bd4\u3092\u63a5\u7d9a\u3059\u308b\u4e09\u89d2\u6052\u7b49\u5f0f\u304b\u3089\u958b\u59cb\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-dbf6d65fa67f0a2161bd99ee7431f015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"124\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u9664\u7b97\u5546\u306e\u5c0e\u95a2\u6570\/\">\u9664\u7b97\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092<\/a><\/span>\u4f7f\u7528\u3059\u308b\u3068\u3001\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-334dc33e2ef413b8d99dd7de50cebc74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\left(\\text{tan}(x)\\right)'=\\left(\\frac{\\text{sen}(x)}{\\text{cos}(x)}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"173\" 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-2b05dcbadd57bacdab9a7d4eda718e3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}(x)\\cdot \\text{cos}(x)+\\text{sen}(x)\\text{sen}(x) }{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"308\" 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-cf6fae22356a5ba2fe4f327843c0da81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}^2(x)+\\text{sen}^2(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"214\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3057\u304b\u3057\u3001\u57fa\u672c\u7684\u306a\u4e09\u89d2\u95a2\u6570\u306e\u6052\u7b49\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u30b5\u30a4\u30f3\u306e 2 \u4e57\u3068\u30b3\u30b5\u30a4\u30f3\u306e 2 \u4e57\u3092\u52a0\u7b97\u3057\u305f\u3082\u306e\u304c 1 \u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\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-92d80771f891319379b2e756c5524aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(x)+\\text{cos}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" 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-c737664b7a2ec3456d700d4939c15806_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{1}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"136\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001\u79c1\u305f\u3061\u306f\u3059\u3067\u306b\u63a5\u7dda\u306e\u5c0e\u95a2\u6570\u306e\u6700\u521d\u306e\u516c\u5f0f\u306b\u5230\u9054\u3057\u3066\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30bb\u30ab\u30f3\u30c8\u306f\u30b3\u30b5\u30a4\u30f3\u306e\u9006\u4e57\u3067\u3042\u308b\u305f\u3081\u30012 \u756a\u76ee\u306e\u5f0f\u3082\u5c0e\u51fa\u3055\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-41f558939bb7b23e97112acb0630c4bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\text{sec}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"131\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u5f8c\u306b\u3001\u63a5\u7dda\u5c0e\u95a2\u6570\u306e 3 \u756a\u76ee\u306e\u898f\u5247\u306f\u3001\u524d\u306e\u30b9\u30c6\u30c3\u30d7\u306e\u5206\u6570\u3092\u5206\u6570\u306e\u5408\u8a08\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u8a3c\u660e\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-cf6fae22356a5ba2fe4f327843c0da81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}^2(x)+\\text{sen}^2(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"214\" 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-187bc0e3bc1c35a7dfd18197b94aa845_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}^2(x)}{\\text{cos}^2(x)}+\\cfrac{\\text{sen}^2(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"216\" 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-257a8cde825ce1b73cf5849d6a387507_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=1+\\text{tan}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\u3001\u6b63\u63a5\u95a2\u6570\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u304b\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u63a5\u7dda\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u305f\u308a\u3001\u6bb5\u968e\u7684\u306b\u89e3\u6c7a\u3055\u308c\u308b\u6f14\u7fd2\u3067\u7df4\u7fd2\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u6b63\u63a5\u5fae\u5206\u516c\u5f0f\u3092\u793a\u3057\u3001\u9006\u6b63\u63a5\u5fae\u5206\u516c\u5f0f\u3082\u793a\u3057\u307e\u3059\u3002 \u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306e\u5c0e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e3%82%bf%e3%83%b3%e3%82%b8%e3%82%a7%e3%83%b3%e3%83%88%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u63a5\u7dda\u306e\u5c0e\u95a2\u6570<\/span> \u3082\u3063\u3068\u8aad\u3080 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