{"id":35217,"date":"2024-12-01T13:00:37","date_gmt":"2024-12-01T13:00:37","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35217"},"modified":"2025-11-22T22:38:44","modified_gmt":"2025-11-22T22:38:44","slug":"%e9%96%a2%e6%95%b0%e5%90%88%e6%88%90%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0%e3%81%ab%e5%af%be%e3%81%99%e3%82%8b%e9%80%a3%e9%8e%96%e6%b3%95%e5%89%87","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e9%96%a2%e6%95%b0%e5%90%88%e6%88%90%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0%e3%81%ab%e5%af%be%e3%81%99%e3%82%8b%e9%80%a3%e9%8e%96%e6%b3%95%e5%89%87\/","title":{"rendered":"\u95a2\u6570\u5408\u6210\u306e\u5c0e\u95a2\u6570\u306b\u5bfe\u3059\u308b\u9023\u9396\u6cd5\u5247"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u95a2\u6570\u5408\u6210\u306e\u5c0e\u95a2\u6570\u306b\u5bfe\u3059\u308b\u9023\u9396\u6cd5\u5247<\/h1>\n<p><em>\u3053\u3053\u307e\u3067\u306b\u5b66\u3093\u3067\u304d\u305f\u5185\u5bb9\u306b\u3088\u308a\u3001\u307b\u3068\u3093\u3069\u3042\u3089\u3086\u308b\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u57fa\u672c\u7684\u306a\u9053\u5177\u306f\u3059\u3067\u306b\u305d\u308d\u3063\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3042\u308b\u5c0e\u95a2\u6570\u3092\u300c\u8a08\u7b97\u3067\u304d\u308b\u300d\u3053\u3068\u3068\u3001\u305d\u306e\u8a08\u7b97\u3092\u5b9f\u969b\u306b\u884c\u3046\u969b\u306b\u5fc5\u8981\u3068\u306a\u308b\u52b4\u529b\u3068\u306f\u533a\u5225\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u305d\u3057\u3066\u3001\u307e\u3055\u306b\u3053\u306e\u70b9\u306b\u304a\u3044\u3066\u30011 \u5909\u6570\u306e\u5834\u5408\u306e\u9023\u9396\u6cd5\u5247\u306a\u3069\u306e\u5b9a\u7406\u304c\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u9023\u9396\u6cd5\u5247\u3092\u7528\u3044\u308c\u3070\u3001\u672c\u6765\u3067\u3042\u308c\u3070\u304b\u306a\u308a\u7169\u96d1\u3067\u9762\u5012\u306a\u8a08\u7b97\u3092\u8981\u3059\u308b\u5c0e\u95a2\u6570\u3092\u3001\u8fc5\u901f\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/em><\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n<b><u>\u76ee\u6b21<\/u><\/b><br \/>\n<b><a href=\"#1\">\u5b9f\u6570\u5024 1 \u5909\u6570\u306b\u304a\u3051\u308b\u9023\u9396\u6cd5\u5247\u306e\u5b9a\u7406<\/a><\/b><br \/>\n<a href=\"#11\">\u9023\u9396\u6cd5\u5247\u306e\u8a3c\u660e<\/a><br \/>\n<a href=\"#12\">\u4e00\u5909\u6570\u95a2\u6570\u306b\u304a\u3051\u308b\u9023\u9396\u6cd5\u5247\u306e\u5229\u7528\u4f8b<\/a><br \/>\n<a href=\"#13\">\u9023\u9396\u6cd5\u5247\u3092\u7528\u3044\u308b\u969b\u306b\u7559\u610f\u3059\u3079\u304d\u70b9<\/a><br \/>\n<b><a href=\"#2\">\u9023\u9396\u6cd5\u5247\u304b\u3089\u5f97\u3089\u308c\u308b\u6709\u7528\u306a\u7d50\u679c<\/a><\/b><br \/>\n<a href=\"#21\">\u9006\u95a2\u6570\u5b9a\u7406<\/a><br \/>\n<a href=\"#211\">\u6307\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570<\/a><br \/>\n<a href=\"#212\">\u9006\u4e09\u89d2\u95a2\u6570\u306e\u5c0e\u95a2\u6570<\/a><br \/>\n<a href=\"#22\">\u9670\u95a2\u6570\u306e\u5fae\u5206<\/a><br \/>\n<a href=\"#221\">\u6709\u7406\u3079\u304d\u306e\u5c0e\u95a2\u6570<\/a><br \/>\n<a href=\"#221\">\u6709\u7406\u3079\u304d\u306e\u5c0e\u95a2\u6570<\/a><br \/>\n<b><a href=\"#3\">\u6f14\u7fd2\u554f\u984c\u96c6<\/a><\/b>\n<\/p>\n<p><a name=\"1\"><\/a><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/0y2SQpbRe3A\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u5b9f\u6570\u5024 1 \u5909\u6570\u306b\u304a\u3051\u308b\u9023\u9396\u6cd5\u5247\u306e\u5b9a\u7406<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=0y2SQpbRe3A&amp;t=165s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u3092\u5408\u6210\u53ef\u80fd\u306a 2 \u3064\u306e\u95a2\u6570\u3068\u3059\u308b<\/span><\/a> susceptibles de composici\u00f3n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f: A\\subseteq \\mathbb{R} \\longmapsto B\\subseteq \\mathbb{R}<\/span>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g: B\\subseteq Dom(g) \\longmapsto D\\subseteq \\mathbb{R}<\/span>\n<p>\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308a\u3001<span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u306a\u3089\u3070\u3001\u5408\u6210\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g\\circ f<\/span><\/span> \u306f\u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in A<\/span><\/span> \u306b\u3064\u3044\u3066\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308a\u3001\u6b21\u306e\u516c\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}(g\\circ f)(x) = \\frac{d}{dx} g(f(x)) = \\frac{dg(f(x))}{df(x)} \\frac{df(x)}{dx}<\/span>\n<p><a name=\"11\"><\/a><\/p>\n<h3>\u9023\u9396\u6cd5\u5247\u306e\u8a3c\u660e<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=0y2SQpbRe3A&amp;t=242s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u95a2\u6570\u3092\u8003\u3048\u308b<\/span><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u3092\u3001\u5148\u306b\u5b9a\u7fa9\u3057\u305f\u3082\u306e\u3068\u540c\u3058\u3068\u3057\u307e\u3059\u3002\u5408\u6210\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\n\\dfrac{d}{dx} g(f(x))&amp; = &amp; \\displaystyle\\lim_{\\Delta x \\to 0} \\dfrac{g(f(x + \\Delta x)) - g(f(x))}{\\Delta x} \\\\ \\\\\n\n&amp;=&amp;\\displaystyle \\lim_{\\Delta x \\to 0} \\frac{g(f(x + \\Delta x)) - g(f(x))}{\\Delta x} \\cdot \\frac{f(x + \\Delta x) - f(x)}{f(x+\\Delta x) - f(x)} \\\\ \\\\\n\n&amp;=&amp; \\displaystyle \\lim_{\\Delta x \\to 0} \\frac{g(f(x + \\Delta x)) - g(f(x))}{f(x+\\Delta x) - f(x)} \\cdot \\frac{f(x + \\Delta x) - f(x)}{\\Delta x} \\\\ \\\\\n\n&amp;=&amp;\\displaystyle \\lim_{\\Delta x \\to 0} \\frac{g(f(x + \\Delta x)) - g(f(x))}{f(x+\\Delta x) - f(x)} \\cdot \\lim_{\\Delta x \\to 0} \\frac{f(x + \\Delta x) - f(x)}{\\Delta x}\\\\ \\\\\n\n&amp;=&amp; \\displaystyle \\lim_{f(x+\\Delta x) \\to f(x) } \\frac{g(f(x + \\Delta x)) - g(f(x))}{f(x+\\Delta x) - f(x)} \\cdot \\lim_{\\Delta x \\to 0} \\frac{f(x + \\Delta x) - f(x)}{\\Delta x}\\\\ \\\\\n\n&amp;=&amp; \\displaystyle \\frac{dg(f(x))}{df(x)} \\frac{df(x)}{dx}\n\n\\end{array}\n\n<\/span>\n<p>\u4ee5\u4e0a\u3067\u8a3c\u660e\u3059\u3079\u304d\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<p><a name=\"12\"><\/a><\/p>\n<h3>\u4e00\u5909\u6570\u95a2\u6570\u306b\u304a\u3051\u308b\u9023\u9396\u6cd5\u5247\u306e\u5229\u7528\u4f8b<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=0y2SQpbRe3A&amp;t=423s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u5c11\u306a\u304f\u3068\u3082\u4e00\u898b\u3059\u308b\u3068\u660e\u3089\u304b\u306a\u3088\u3046\u306b\u601d\u308f\u308c\u308b\u3053\u3068<\/span><\/a> \u3067\u3059\u304c\u3001\u64cd\u4f5c\u7684\u306a\u89b3\u70b9\u304b\u3089\u306f\u5fc5\u305a\u3057\u3082\u81ea\u660e\u3067\u306f\u306a\u3044\u70b9\u3068\u3057\u3066\u3001\u9023\u9396\u6cd5\u5247\u306f\u300c\u95a2\u6570\u306e\u5408\u6210\u306b\u51fa\u4f1a\u3063\u305f\u3068\u304d\u3001\u5916\u5074\u304b\u3089\u5185\u5074\u3078\u3068\u5fae\u5206\u3057\u3066\u3088\u3044\u300d\u3068\u3044\u3046\u4e8b\u5b9f\u3092\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3092\u3088\u308a\u7406\u89e3\u3057\u3084\u3059\u304f\u8aac\u660e\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u4f8b\u3092\u7528\u3044\u308b\u306e\u304c\u6700\u3082\u901f\u304f\u3001\u304b\u3064\u5206\u304b\u308a\u3084\u3059\u3044\u65b9\u6cd5\u3067\u3059\u3002<\/p>\n<ol>\n<li>\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = (2x^2+1)^{12}<\/span><\/span> \u3092\u5fae\u5206\u305b\u3088\u3068\u8a00\u308f\u308c\u305f\u5834\u5408\u3001\u307e\u305a\u51aa\u3092\u5c55\u958b\u3057\u3001\u305d\u306e\u5f8c\u3067\u5f97\u3089\u308c\u305f\u5de8\u5927\u306a\u591a\u9805\u5f0f\u306e\u5404\u90e8\u5206\u306b\u5bfe\u3057\u3066\u51aa\u95a2\u6570\u306e\u5fae\u5206\u3092\u9069\u7528\u3059\u308b\u3001\u3068\u3044\u3046\u624b\u9806\u3092\u8e0f\u3080\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u4e0d\u5fc5\u8981\u306b\u52b4\u529b\u306e\u304b\u304b\u308b\u65b9\u6cd5\u3067\u3059\u3002\u9023\u9396\u6cd5\u5247\u3092\u4f7f\u3048\u3070\u3001\u5c0e\u95a2\u6570\u306e\u8a08\u7b97\u306f\u6b21\u306e\u3088\u3046\u306b\u6570\u884c\u3067\u6e08\u307f\u307e\u3059\uff1a<br \/>\n<\/p>\n<p style=\"align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx} (2x^2+1)^{12} = 12(2x^2+1)^{11}(4x)= 48x(2x^2+1)^{11}<\/span>\n<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\sin(\\cos(x))<\/span><\/span> \u306e\u5c0e\u95a2\u6570\u3092\u57fa\u672c\u7684\u306a\u5fae\u5206\u6280\u6cd5\u3060\u3051\u3067\u8a08\u7b97\u3057\u3088\u3046\u3068\u3059\u308c\u3070\u3001\u6c38\u9060\u306e\u82e6\u3057\u307f\u306b\u76f4\u9762\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u9023\u9396\u6cd5\u5247\u3092\u4f7f\u3048\u3070\u3001\u6d99\u3092\u6d41\u3059\u3053\u3068\u306a\u304f\u6570\u30b9\u30c6\u30c3\u30d7\u3067\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<br \/>\n<\/p>\n<p style=\"align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx} \\sin(\\cos(x))= -\\cos(cos(x))\\sin(x) <\/span>\n<\/li>\n<li>\u307e\u305f\u3001\u591a\u304f\u306e\u95a2\u6570\u3092\u91cd\u306d\u5408\u308f\u305b\u305f\u5408\u6210\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3082\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\cos(\\cos(\\cos(x))),<\/span><\/span> \u3068\u3059\u308c\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">df\/dx<\/span><\/span> \u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<br \/>\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\n\\displaystyle \\frac{d}{dx} \\cos(\\cos(\\cos(x))) &amp;=&amp; -\\sin(\\cos(\\cos(x)))\\cdot(-\\sin(\\cos(x))\\cdot(-\\sin(x)) \\\\ \\\\\n\n&amp;=&amp; -\\sin(\\cos(\\cos(x)))\\cdot\\sin(\\cos(x))\\cdot\\sin(x)\n\n\\end{array}\n\n<\/span>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u9023\u9396\u6cd5\u5247\u3092\u9069\u7528\u3059\u308b\u3068\u306f\u3001\u5916\u5074\u304b\u3089\u5185\u5074\u3078\u3068\u9806\u306b\u5fae\u5206\u3092\u91cd\u306d\u3066\u3044\u304f\u3053\u3068\u306b\u4ed6\u306a\u308a\u307e\u305b\u3093\u3002<\/li>\n<\/ol>\n<p><a name=\"13\"><\/a><\/p>\n<h3>\u9023\u9396\u6cd5\u5247\u306b\u95a2\u3057\u3066\u7559\u610f\u3059\u3079\u304d\u70b9<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=0y2SQpbRe3A&amp;t=607s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u6587\u732e\u3067\u306f\u3001\u9023\u9396\u6cd5\u5247\u306e\u5927\u304d\u306a\u5229\u70b9\u304c\u7e70\u308a\u8fd4\u3057\u5f37\u8abf\u3055\u308c\u3066\u3044\u307e\u3059<\/span><\/a> \u304c\u3001\u305d\u306e\u4f7f\u7528\u306b\u5148\u7acb\u3063\u3066\u5fc5\u8981\u3068\u306a\u308b\u6ce8\u610f\u70b9\u3092\u5f37\u8abf\u3059\u308b\u3082\u306e\u306f\u591a\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u305f\u3068\u3048\u3053\u306e\u5b9a\u7406\u304c\u5f37\u529b\u3067\u3042\u3063\u3066\u3082\u3001\u9023\u9396\u6cd5\u5247\u3092\u7528\u3044\u308b\u524d\u306b\u306f\u3001\u5e38\u306b\u95a2\u6570\u306e\u5b9a\u7fa9\u57df\uff08\u30c9\u30e1\u30a4\u30f3\uff09\u3068\u5024\u57df\uff08\u30ec\u30f3\u30b8\uff09\u306b\u7d30\u5fc3\u306e\u6ce8\u610f\u3092\u6255\u308f\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u4f5c\u696d\u306b\u5165\u308b\u524d\u306b\u3001\u95a2\u6570\u540c\u58eb\u306e\u5b9a\u7fa9\u57df\u3068\u5024\u57df\u304c\u5408\u6210\u306b\u9069\u5408\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3046\u3057\u306a\u3044\u3068\u3001\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3057\u3066\u3057\u307e\u3046\u5371\u967a\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6b21\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u5834\u5408\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\ln(\\cos(x))<\/span>\n<p>\u3082\u3057\u9023\u9396\u6cd5\u5247\u3092\u76f2\u76ee\u7684\u306b\u4fe1\u3058\u3066\u3057\u307e\u3046\u3068\u3001\u6b21\u306e\u3088\u3046\u306a\u8a08\u7b97\u3092\u884c\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\ln(\\cos(x)) = -\\frac{1}{\\cos(x)}\\sin(x) = -\\tan(x)<\/span>\n<p>\u660e\u3089\u304b\u306b\u3001\u6b63\u63a5\u95a2\u6570\uff08\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\uff09\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x=2\\pi\/3<\/span><\/span> \u3067\u3088\u304f\u5b9a\u7fa9\u3055\u308c\u3066\u304a\u308a\u3001\u305d\u306e\u5024\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tan(2\\pi\/3) = -\\sqrt{3}<\/span><\/span> \u3067\u3059\u3002\u3057\u304b\u3057\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\ln(\\cos(x))<\/span><\/span> \u306f\u305d\u306e\u70b9\u3067\u306f\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u3068\u3044\u3046\u306e\u3082\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(2\\pi\/3) = \\ln(\\cos(2\\pi\/3)) = \\ln(-1\/2),<\/span><\/span> \u3068\u306a\u308a\u3001\u8ca0\u306e\u6570\u306e\u5bfe\u6570\u306f\u5b58\u5728\u3057\u306a\u3044\u305f\u3081\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u306b\u306f\u3001\u9023\u9396\u6cd5\u5247\u3092\u9069\u7528\u3059\u308b\u524d\u306b\u3001\u8003\u3048\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u306e\u5024\u304c\u4f59\u5f26\u95a2\u6570\u3092\u6b63\u306b\u4fdd\u3064\u7bc4\u56f2\u306b\u5c5e\u3059\u308b\u3053\u3068\u3092\u660e\u793a\u3057\uff08\u3059\u306a\u308f\u3061\u3001\u5408\u6210\u304c\u9069\u5408\u3059\u308b\u3088\u3046\u306b\u3057\uff09\u3001\u305d\u306e\u3046\u3048\u3067\u521d\u3081\u3066\u9023\u9396\u6cd5\u5247\u304c\u6210\u7acb\u3059\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u9023\u9396\u6cd5\u5247\u304b\u3089\u5f97\u3089\u308c\u308b\u6709\u7528\u306a\u7d50\u679c<\/h2>\n<p>\u9023\u9396\u6cd5\u5247\u306f\u3001\u4ed6\u306e\u65b9\u6cd5\u3067\u306f\u8a08\u7b97\u304c\u975e\u5e38\u306b\u56f0\u96e3\u306b\u306a\u308b\u5c0e\u95a2\u6570\u306e\u8a08\u7b97\u3092\u5bb9\u6613\u306b\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u591a\u304f\u306e\u95a2\u6570\u306b\u5bfe\u3057\u3066\u5fae\u5206\u306e\u6280\u6cd5\u3092\u62e1\u5f35\u3059\u308b\u969b\u306b\u3082\u5f79\u7acb\u3061\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u6280\u6cd5\u3068\u305d\u306e\u7d50\u679c\u3001\u3055\u3089\u306b\u8a3c\u660e\u3092\u78ba\u8a8d\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<p><a name=\"21\"><\/a><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/5ddoUcIhgjU\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><a name=\"21\"><\/a><\/p>\n<h3>\u9006\u95a2\u6570\u5b9a\u7406<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=5ddoUcIhgjU&amp;t=75s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u3092\u5168\u5358\u5c04\uff08\u53cc\u5c04\uff09<\/span><\/a> \u3068\u3057\u3001\u3042\u308b\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq \\mathbb{R}<\/span><\/span> \u3067\u5fae\u5206\u53ef\u80fd\u3068\u3057\u307e\u3059\u3002\u9023\u9396\u6cd5\u5247\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u6052\u7b49\u5199\u50cf <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(f^{-1}\\circ f)(x) = f^{-1}(f(x)) = x.<\/span><\/span> \u306e\u5c0e\u95a2\u6570\u306e\u8a08\u7b97\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u8a08\u7b97\u3059\u308b\u3068\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1 = \\displaystyle \\frac{d}{dx} x = \\frac{d}{dx} f^{-1}(f(x)) = \\frac{df^{-1}(f(x))}{df(x)}\\frac{df(x)}{dx}<\/span>\n<p>\u3053\u3053\u304b\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">df^{-1}(f(x))\/df(x)<\/span><\/span> \u3092\u89e3\u304f\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{df^{-1}(f(x))}{df(x)}= \\frac{1}{\\frac{df(x)}{dx}}}<\/span>\n<p>\u3053\u308c\u306f\u5c0e\u95a2\u6570\u306e\u8a08\u7b97\u306b\u304a\u3051\u308b\u9006\u95a2\u6570\u5b9a\u7406\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u6587\u732e\u3067\u306f\u3001\u3053\u306e\u5b9a\u7406\u304c\u6b21\u306e\u5f62\u3067\u66f8\u304b\u308c\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{dx}{dy}= \\frac{1}{\\frac{dy}{dx}}}<\/span>\n<p>\u3053\u308c\u3089 2 \u3064\u306e\u5f62\u5f0f\u306f\u7b49\u4fa1\u3067\u3042\u308a\u3001\u5358\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=f(x)<\/span><\/span>\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x=f^{-1}(y).<\/span><\/span> \u3068\u66f8\u304d\u63db\u3048\u305f\u3082\u306e\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u307e\u3067\u3067\u9006\u95a2\u6570\u5b9a\u7406\u306e\u5185\u5bb9\u3092\u6982\u89b3\u3057\u307e\u3057\u305f\u3002\u6b21\u306b\u3001\u3053\u306e\u5b9a\u7406\u3092\u3069\u306e\u3088\u3046\u306b\u6d3b\u7528\u3057\u3066\u3001\u901a\u5e38\u3067\u306f\u304b\u306a\u308a\u96e3\u3057\u3044\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3067\u304d\u308b\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<p><a name=\"211\"><\/a><\/p>\n<h4>\u6307\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570<\/h4>\n<p><span style=\"color: #ff0000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=5ddoUcIhgjU&amp;t=215s\" target=\"_blank\" style=\"color: #ff0000;\" rel=\"noopener\">\u57fa\u672c\u7684\u306a\u5fae\u5206\u6280\u6cd5\u3092\u5b66\u3093\u3060\u3068\u304d\u3001<\/a><\/span> \u6b21\u306e\u516c\u5f0f\u3092\u898b\u307e\u3057\u305f\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\ln(x) = \\frac{1}{x}<\/span>\n<p>\u3053\u306e\u7d50\u679c\u3068\u9006\u95a2\u6570\u5b9a\u7406\u3092\u7528\u3044\u308b\u3068\u3001\u6b21\u3092\u793a\u3059\u306e\u306f\u5bb9\u6613\u3067\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}e^x = e^x<\/span>\n<p style=\"text-align: justify;color: #000080;\"><strong>\u8a3c\u660e\uff1a<\/strong><\/p>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\ln(x)<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x=e^y<\/span><\/span> \u3068\u8a00\u3046\u3053\u3068\u3068\u540c\u5024\u3067\u3059\u3002\u3088\u3063\u3066\u3001\u9006\u95a2\u6570\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3068\u6b21\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}e^y = \\frac{dx}{dy} = \\frac{1}{\\frac{dy}{dx}} = \\frac{1}{\\frac{d}{dx}\\ln(x)} = x = e^y<\/span>\n<p>\u3064\u307e\u308a\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}e^y = e^y<\/span>\n<p>\u3053\u306e\u6700\u5f8c\u306e\u5f0f\u306b\u304a\u3044\u3066\u3001\u00bby\u00bb \u3092 \u00abx\u00bb \u306b\u7f6e\u304d\u63db\u3048\u308c\u3070\u3001\u793a\u3059\u3079\u304d\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}e^x = e^x.<\/span>\n<p><a name=\"212\"><\/a><\/p>\n<h4>\u9006\u4e09\u89d2\u95a2\u6570\u306e\u5c0e\u95a2\u6570<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=5ddoUcIhgjU\" target=\"\" span=\"\" style=\"color: #ff0000;\" 0=\"\" a=\"\">\u9006\u95a2\u6570\u5b9a\u7406<\/a> \u306f\u3001\u9006\u4e09\u89d2\u95a2\u6570\u3059\u3079\u3066\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u969b\u306b\u3082\u5229\u7528\u3067\u304d\u307e\u3059\u3002\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{ccccccc}\n\n\\dfrac{d}{dx}\\text{Arcsin}(x) &amp;=&amp; \\dfrac{1}{\\sqrt{1-x^2}} &amp;\\phantom{asd}&amp;\\dfrac{d}{dx}\\text{Arccos}(x) &amp;=&amp; \\dfrac{-1}{\\sqrt{1-x^2}} \\\\ \\\\\n\n\\dfrac{d}{dx}\\text{Arctan}(x) &amp;=&amp; \\dfrac{1}{1+x^2} &amp;\\phantom{asd}&amp;\\dfrac{d}{dx}\\text{Arccot}(x) &amp;=&amp; \\dfrac{-1}{1-x^2} \\\\ \\\\\n\n\\dfrac{d}{dx}\\text{Arcsec}(x) &amp;=&amp; \\dfrac{1}{x\\sqrt{x^2-1}} &amp;\\phantom{asd}&amp;\\dfrac{d}{dx}\\text{Arccsc}(x) &amp;=&amp; \\dfrac{-1}{x\\sqrt{x^2-1}}\n\n\\end{array}<\/span>\n<p style=\"text-align: justify; color: #000080;\"><strong>\u8a3c\u660e<\/strong><\/p>\n<h5>\u30a2\u30fc\u30af\u30b5\u30a4\u30f3<\/h5>\n<span class=\"collapseomatic \" id=\"id69e3fd4745f80\"  tabindex=\"0\" title=\"\u8a3c\u660e\u3092\u8868\u793a\"    >\u8a3c\u660e\u3092\u8868\u793a<\/span><div id=\"target-id69e3fd4745f80\" class=\"collapseomatic_content \">\n<p>\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin(x)<\/span><\/span> \u306f\u3001\u305d\u306e\u5b9a\u7fa9\u57df\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[\\frac{-\\pi}{2}+k\\pi , \\frac{\\pi}{2}+ k\\pi \\right]<\/span><\/span>\uff08\u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306f\u4efb\u610f\u306e\u6574\u6570\uff09\u306b\u5236\u9650\u3059\u308c\u3070\u5358\u5c04\u304b\u3064\u5168\u5c04\uff08\u53cc\u5c04\uff09\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u6027\u3092\u5931\u3046\u3053\u3068\u306a\u304f\u4e3b\u5024\u9818\u57df <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0<\/span><\/span> \u306e\u5834\u5408\u306b\u9650\u5b9a\u3059\u308b\u3068\u3001\u53cc\u5c04\u3068\u306a\u308b\u6b63\u5f26\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\sin : \\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right] \\longrightarrow [-1,1]<\/span>\n<p>\u3053\u306e\u3068\u304d\u3001\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u7acb\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\sin(x) \\longleftrightarrow x=arcsin(y).<\/span>\n<p>\u9006\u95a2\u6570\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3068\u6b21\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arcsin(y) = \\frac{1}{\\frac{d}{dx}\\sin(x)} = \\frac{1}{\\cos(x)}<\/span>\n<p>\u3053\u3053\u3067\u3001\u4e09\u89d2\u6052\u7b49\u5f0f<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin^2(x) + \\cos^2(x) = 1<\/span>\n<p>\u3092\u601d\u3044\u51fa\u3059\u3068\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in [-\\pi\/2, \\pi\/2]<\/span><\/span> \u3067\u3042\u308c\u3070\u6b21\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\cos(x) = \\sqrt{1 - \\sin^2(x)}<\/span>\n<p>\u3053\u308c\u3092\u5148\u307b\u3069\u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arcsin(y) = \\frac{1}{\\cos(x)} = \\frac{1}{ \\sqrt{1 - \\sin^2(x)}}<\/span>\n<p>\u3055\u3089\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\sin(x)<\/span><\/span> \u3092\u7528\u3044\u3066\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arcsin(y) = \\frac{1}{ \\sqrt{1 - y^2}}<\/span>\n<p>\u6700\u5f8c\u306b\u3001\u3053\u306e\u5f0f\u306e \u00aby\u00bb \u3092 \u00abx\u00bb \u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001\u793a\u3059\u3079\u304d\u7d50\u8ad6\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{d}{dx}arcsin(x) = \\frac{1}{ \\sqrt{1 - x^2}}}<\/span>\n<\/div>\n<h5>\u30a2\u30fc\u30af\u30b3\u30b5\u30a4\u30f3<\/h5>\n<span class=\"collapseomatic \" id=\"id69e3fd4746245\"  tabindex=\"0\" title=\"\u8a3c\u660e\u3092\u8868\u793a\"    >\u8a3c\u660e\u3092\u8868\u793a<\/span><div id=\"target-id69e3fd4746245\" class=\"collapseomatic_content \">\n<p>\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\cos(x)<\/span><\/span> \u306f\u3001\u305d\u306e\u5b9a\u7fa9\u57df\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left[0+k\\pi , \\pi+ k\\pi \\right]<\/span><\/span>\uff08\u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306f\u4efb\u610f\u306e\u6574\u6570\uff09\u306b\u5236\u9650\u3059\u308c\u3070\u53cc\u5c04\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u6027\u3092\u5931\u3046\u3053\u3068\u306a\u304f\u4e3b\u5024\u9818\u57df <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0<\/span><\/span> \u306e\u5834\u5408\u306b\u9650\u5b9a\u3059\u308b\u3068\u3001\u53cc\u5c04\u3068\u306a\u308b\u4f59\u5f26\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\cos : \\left[0, \\pi\\right] \\longrightarrow [-1,1]<\/span>\n<p>\u3053\u306e\u3068\u304d\u3001\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u7acb\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\cos(x) \\longleftrightarrow x=arccos(y).<\/span>\n<p>\u9006\u95a2\u6570\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arccos(y) = \\frac{1}{\\frac{d}{dx}\\cos(x)} = \\frac{-1}{\\sin(x)}<\/span>\n<p>\u6b21\u306b\u4e09\u89d2\u6052\u7b49\u5f0f<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin^2(x) + \\cos^2(x) = 1<\/span>\n<p>\u3088\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in [0, \\pi]<\/span><\/span> \u306e\u3068\u304d\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\sin(x) = \\sqrt{1 - \\cos^2(x)}<\/span>\n<p>\u3053\u308c\u3092\u4ee3\u5165\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arccos(y) = \\frac{-1}{\\sin(x)} = \\frac{-1}{ \\sqrt{1 - \\cos^2(x)}}<\/span>\n<p>\u3055\u3089\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\cos(x)<\/span><\/span> \u3067\u3042\u308b\u304b\u3089\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arccos(y) = \\frac{-1}{ \\sqrt{1 - y^2}}<\/span>\n<p>\u6700\u5f8c\u306b\u3001\u00bby\u00bb \u3092 \u00abx\u00bb \u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u793a\u3059\u3079\u304d\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{d}{dx}arccos(x) = \\frac{-1}{ \\sqrt{1 - x^2}}}<\/span>\n<\/div>\n<h5>\u30a2\u30fc\u30af\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8<\/h5>\n<span class=\"collapseomatic \" id=\"id69e3fd47463d0\"  tabindex=\"0\" title=\"\u8a3c\u660e\u3092\u8868\u793a\"    >\u8a3c\u660e\u3092\u8868\u793a<\/span><div id=\"target-id69e3fd47463d0\" class=\"collapseomatic_content \">\n<p>\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tan(x)<\/span><\/span> \u306f\u3001\u305d\u306e\u5b9a\u7fa9\u57df\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[-\\frac{\\pi}{2}+k\\pi , \\frac{\\pi}{2}+ k\\pi \\right]<\/span><\/span>\uff08\u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306f\u4efb\u610f\u306e\u6574\u6570\uff09\u306b\u5236\u9650\u3059\u308c\u3070\u53cc\u5c04\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u6027\u3092\u5931\u3046\u3053\u3068\u306a\u304f\u4e3b\u5024\u9818\u57df <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0<\/span><\/span> \u306b\u9650\u5b9a\u3059\u308b\u3068\u3001\u53cc\u5c04\u3068\u306a\u308b\u6b63\u63a5\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\tan : \\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right] \\longrightarrow \\mathbb{R}<\/span>\n<p>\u3053\u306e\u3068\u304d\u3001\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u7acb\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\tan(x) \\longleftrightarrow x=arctan(y).<\/span>\n<p>\u9006\u95a2\u6570\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arctan(y) = \\frac{1}{\\frac{d}{dx}\\tan(x)} = \\frac{1}{\\sec^2(x)}<\/span>\n<p>\u3055\u3089\u306b\u3001\u4e09\u89d2\u6052\u7b49\u5f0f<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin^2(x) + \\cos^2(x) = 1<\/span>\n<p>\u3088\u308a\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\sec^2(x) =1+\\tan^2(x)<\/span>\n<p>\u3053\u308c\u3092\u4ee3\u5165\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arctan(y) = \\frac{1}{\\sec^2(x)} = \\frac{1}{ 1+\\tan^2(x)}<\/span>\n<p>\u3055\u3089\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\tan(x)<\/span><\/span> \u3092\u7528\u3044\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arctan(y) = \\frac{1}{1 + y^2}<\/span>\n<p>\u6700\u5f8c\u306b\u3001\u3053\u306e\u5f0f\u306e \u00aby\u00bb \u3092 \u00abx\u00bb \u306b\u7f6e\u304d\u63db\u3048\u308c\u3070\u3001\u793a\u3059\u3079\u304d\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{d}{dx}arctan(x) = \\frac{1}{1+ x^2}}<\/span>\n<\/div>\n<h5>\u30a2\u30fc\u30af\u30b3\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8<\/h5>\n<span class=\"collapseomatic \" id=\"id69e3fd474652b\"  tabindex=\"0\" title=\"\u8a3c\u660e\u3092\u8868\u793a\"    >\u8a3c\u660e\u3092\u8868\u793a<\/span><div id=\"target-id69e3fd474652b\" class=\"collapseomatic_content \">\n<p>\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">cot(x)<\/span><\/span> \u306f\u3001\u305d\u306e\u5b9a\u7fa9\u57df\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left[0+k\\pi , \\pi+ k\\pi \\right]<\/span><\/span>\uff08\u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306f\u4efb\u610f\u306e\u6574\u6570\uff09\u306b\u5236\u9650\u3059\u308c\u3070\u53cc\u5c04\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u6027\u3092\u5931\u3046\u3053\u3068\u306a\u304f\u4e3b\u5024\u9818\u57df <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0<\/span><\/span> \u306e\u5834\u5408\u306b\u9650\u5b9a\u3059\u308b\u3068\u3001\u53cc\u5c04\u3068\u306a\u308b\u4f59\u63a5\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ctg : \\left[0, \\pi\\right] \\longrightarrow \\mathbb{R}<\/span>\n<p>\u3053\u306e\u3068\u304d\u6b21\u304c\u6210\u7acb\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=ctg(x) \\longleftrightarrow x=arcctg(y).<\/span>\n<p>\u9006\u95a2\u6570\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arcctg(y) = \\frac{1}{\\frac{d}{dx}ctg(x)} = \\frac{-1}{\\csc^2(x)}<\/span>\n<p>\u6b21\u306b\u4e09\u89d2\u6052\u7b49\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin^2(x) + \\cos^2(x) = 1<\/span>\n<p>\u3088\u308a\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\csc^2(x) =1+ctg^2(x)<\/span>\n<p>\u3053\u308c\u3092\u4ee3\u5165\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arcctg(y) = \\frac{-1}{\\csc^2(x)} = \\frac{-1}{ 1+ctg^2(x)}<\/span>\n<p>\u3055\u3089\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=ctg(x)<\/span><\/span> \u3092\u4f7f\u3046\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}arcctg(y) = \\frac{-1}{1 + y^2}<\/span>\n<p>\u6700\u5f8c\u306b\u3001\u3053\u306e\u5f0f\u306e \u00aby\u00bb \u3092 \u00abx\u00bb \u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{d}{dx}arcctg(x) = \\frac{-1}{1+ x^2}}<\/span>\n<\/div>\n<h5>\u30a2\u30fc\u30af\u30bb\u30ab\u30f3\u30c8<\/h5>\n<span class=\"collapseomatic \" id=\"id69e3fd4746675\"  tabindex=\"0\" title=\"\u8a3c\u660e\u3092\u8868\u793a\"    >\u8a3c\u660e\u3092\u8868\u793a<\/span><div id=\"target-id69e3fd4746675\" class=\"collapseomatic_content \">\n<p>\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sec(x)<\/span><\/span> \u306f\u3001\u305d\u306e\u5b9a\u7fa9\u57df\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[0+k\\pi , \\pi+ k\\pi \\right]\\setminus\\left\\{\\frac{\\pi}{2} + k\\pi\\right\\}<\/span><\/span>\uff08\u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306f\u4efb\u610f\u306e\u6574\u6570\uff09\u306b\u5236\u9650\u3059\u308c\u3070\u53cc\u5c04\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u6027\u3092\u5931\u3046\u3053\u3068\u306a\u304f\u4e3b\u5024\u9818\u57df <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0<\/span><\/span> \u306b\u9650\u5b9a\u3059\u308b\u3068\u3001\u53cc\u5c04\u3068\u306a\u308b\u6b63\u5272\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sec : \\left[0, \\pi\\right]\\setminus\\{\\pi\/2\\} \\longrightarrow \\mathbb{R}\\setminus]-1,1[<\/span>\n<p>\u3053\u306e\u3068\u304d\u3001\u6b21\u304c\u6210\u7acb\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\sec(x) \\longleftrightarrow x={arcsec}(y).<\/span>\n<p>\u9006\u95a2\u6570\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}{arcsec}(y) = \\frac{1}{\\frac{d}{dx}\\sec(x)} = \\frac{1}{\\sec(x)\\tan(x)}<\/span>\n<p>\u6b21\u306b\u4e09\u89d2\u6052\u7b49\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin^2(x) + \\cos^2(x) = 1<\/span>\n<p>\u3088\u308a\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\tan^2(x) =\\sec^2(x)-1<\/span>\n<p>\u3053\u308c\u3092\u4ee3\u5165\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}{arcsec}(y) = \\frac{1}{\\sec(x)\\tan(x)} = \\frac{1}{sec(x)\\sqrt{\\sec^2(x)-1}}<\/span>\n<p>\u3055\u3089\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\sec(x)<\/span><\/span> \u3092\u7528\u3044\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}{arcsec}(y) = \\frac{1}{y\\sqrt{y^2-1}}<\/span>\n<p>\u6700\u5f8c\u306b\u3001\u3053\u306e\u5f0f\u306e \u00aby\u00bb \u3092 \u00abx\u00bb \u306b\u7f6e\u304d\u63db\u3048\u308c\u3070\u3001\u793a\u3059\u3079\u304d\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{d}{dx}{arcsec}(x) = \\frac{1}{x\\sqrt{x^2-1}}}<\/span>\n<\/div>\n<h5>\u30a2\u30fc\u30af\u30b3\u30bb\u30ab\u30f3\u30c8<\/h5>\n<span class=\"collapseomatic \" id=\"id69e3fd474682f\"  tabindex=\"0\" title=\"\u8a3c\u660e\u3092\u8868\u793a\"    >\u8a3c\u660e\u3092\u8868\u793a<\/span><div id=\"target-id69e3fd474682f\" class=\"collapseomatic_content \">\n<p>\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\csc(x)<\/span><\/span> \u306f\u3001\u305d\u306e\u5b9a\u7fa9\u57df\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left[-\\frac{\\pi}{2}+k\\pi , \\frac{\\pi}{2} + k\\pi \\right]\\setminus\\left\\{0+k\\pi\\right\\}<\/span><\/span>\uff08\u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u306f\u4efb\u610f\u306e\u6574\u6570\uff09\u306b\u5236\u9650\u3059\u308c\u3070\u53cc\u5c04\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u6027\u3092\u5931\u3046\u3053\u3068\u306a\u304f\u4e3b\u5024\u9818\u57df <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0<\/span><\/span> \u306b\u9650\u5b9a\u3059\u308b\u3068\u3001\u53cc\u5c04\u3068\u306a\u308b\u4f59\u5272\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\csc : \\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right]\\setminus\\{0\\} \\longrightarrow \\mathbb{R}\\setminus]-1,1[<\/span>\n<p>\u3053\u306e\u3068\u304d\u6b21\u304c\u6210\u7acb\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\csc(x) \\longleftrightarrow x={arccsc}(y).<\/span>\n<p>\u9006\u95a2\u6570\u5b9a\u7406\u3092\u9069\u7528\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}{arccsc}(y) = \\frac{1}{\\frac{d}{dx}\\csc(x)} = \\frac{-1}{\\csc(x)ctg(x)}<\/span>\n<p>\u6b21\u306b\u4e09\u89d2\u6052\u7b49\u5f0f\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sin^2(x) + \\cos^2(x) = 1<\/span>\n<p>\u3088\u308a\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> ctg^2(x) =\\csc^2(x)-1<\/span>\n<p>\u3053\u308c\u3092\u4ee3\u5165\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}{arcsec}(y) = \\frac{-1}{\\csc(x)ctg(x)} = \\frac{-1}{csc(x)\\sqrt{\\csc^2(x)-1}}<\/span>\n<p>\u3055\u3089\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\csc(x)<\/span><\/span> \u3092\u4f7f\u3046\u3068\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dy}{arccsc}(y) = \\frac{-1}{y\\sqrt{y^2-1}}<\/span>\n<p>\u6700\u5f8c\u306b\u3001\u3053\u306e\u5f0f\u306e \u00aby\u00bb \u3092 \u00abx\u00bb \u306b\u7f6e\u304d\u63db\u3048\u308c\u3070\u3001\u793a\u3059\u3079\u304d\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{d}{dx}{arccsc}(x) = \\frac{-1}{x\\sqrt{x^2-1}}}<\/span>\n<\/div>\n<p><a name=\"22\"><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/hOAydWcd6zw\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/a><\/p>\n<h3>\u9670\u95a2\u6570\u306e\u5fae\u5206<\/h3>\n<p>\u3053\u308c\u307e\u3067\u8a08\u7b97\u3057\u3066\u304d\u305f\u5c0e\u95a2\u6570\u306f\u3059\u3079\u3066\u3001\u660e\u793a\u7684\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=f(x)<\/span><\/span> \u306b\u5bfe\u3057\u3066\u884c\u3063\u3066\u304d\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u5909\u6570\u540c\u58eb\u306e\u95a2\u4fc2\u304c\u4e0e\u3048\u3089\u308c\u3066\u3082\u3001\u95a2\u6570\u3092\u967d\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u96e3\u3057\u3044\u5834\u5408\u3084\u3001\u305d\u3082\u305d\u3082\u89e3\u3051\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u72b6\u6cc1\u3067\u5f79\u7acb\u3064\u306e\u304c\u9670\u95a2\u6570\u306e\u5fae\u5206\u3067\u3042\u308a\u3001\u305d\u306e\u57fa\u790e\u306b\u3082\u3084\u306f\u308a\u9023\u9396\u6cd5\u5247\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u6280\u6cd5\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\u3001\u8a3c\u660e\u3088\u308a\u3082\u4f8b\u3092\u898b\u308b\u65b9\u304c\u306f\u308b\u304b\u306b\u6709\u76ca\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u5909\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u306e\u95a2\u4fc2\u304c\u6b21\u306e\u7b49\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x^3 +y^3- 9xy=0<\/span>\n<p>\u3053\u306e\u95a2\u4fc2\u3092\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u3001\u305d\u308c\u306f\u3069\u306e\u3088\u3046\u306a\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3067\u3082\u306a\u304f\u3001\u300c\u30c7\u30ab\u30eb\u30c8\u306e\u8449\uff08hoja de Descartes\uff09\u300d\u3068\u547c\u3070\u308c\u308b\u66f2\u7dda\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-l30tAMcTkk0\/YLCIuWcDueI\/AAAAAAAAFIY\/K7uSR44DepgIjBlSVV7mCQO-Z0iy_RnRQCLcBGAsYHQ\/s0\/hojaDeDescartes.PNG\" alt=\"hoja de descartes\" class=\"alignnone size-full lazyload\" width=\"690\" height=\"515\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-l30tAMcTkk0\/YLCIuWcDueI\/AAAAAAAAFIY\/K7uSR44DepgIjBlSVV7mCQO-Z0iy_RnRQCLcBGAsYHQ\/s0\/hojaDeDescartes.PNG\" alt=\"hoja de descartes\" class=\"alignnone size-full lazyload\" width=\"690\" height=\"515\" \/><\/noscript><\/center><\/p>\n<p>\u3055\u3066\u3001\u4f8b\u3048\u3070 <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u3092 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u3067\u5fae\u5206\u3057\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u65b9\u7a0b\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=f(x)<\/span><\/span> \u3092\u6e80\u305f\u3059\u660e\u793a\u7684\u306a\u95a2\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u56f0\u96e3\u3067\u3042\u308a\u3001\u305d\u306e\u5f8c\u3067\u5fae\u5206\u3059\u308b\u306e\u306f\u4e8b\u5b9f\u4e0a\u4e0d\u53ef\u80fd\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u5b9f\u969b\u306b\u306f\u305d\u306e\u6bb5\u968e\u3092\u7701\u7565\u3057\u3001<span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u304c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u306e\u95a2\u6570\u3067\u3042\u308b\u3068\u6697\u9ed9\u306b\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3064\u307e\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=y(x)<\/span><\/span> \u3068\u3059\u308b\u306e\u3067\u3059\u3002\u3053\u3046\u3059\u308b\u3068\u3001\u30c7\u30ab\u30eb\u30c8\u306e\u8449\u306b\u5bfe\u3059\u308b\u95a2\u4fc2\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x^3 +y^3(x)- 9xy(x)=0<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u9023\u9396\u6cd5\u5247\u3092\u7528\u3044\u308c\u3070\u5168\u4f53\u3092\u5fae\u5206\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3092\u5b9f\u884c\u3059\u308b\u3068\u6b21\u306e\u7d50\u679c\u306b\u5230\u9054\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\n\\displaystyle 3x^{2} + 3\\,y(x)^{2}\\,\\frac{dy}{dx} - \\left(9\\,y(x) + 9x\\,\\frac{dy}{dx}\\right) &amp;=&amp; 0 \\\\ \\\\\n\n\\displaystyle 3x^{2} + 3\\,y(x)^{2}\\,\\frac{dy}{dx} - 9\\,y(x) - 9x\\,\\frac{dy}{dx} &amp;=&amp; 0 \\\\ \\\\\n\n\\displaystyle \\frac{dy}{dx}\\,\\big(3\\,y(x)^{2} - 9x\\big) &amp;=&amp; 9\\,y(x) - 3x^{2} \\\\ \\\\\n\n\\displaystyle \\frac{dy}{dx} &amp;=&amp; \\dfrac{9\\,y(x) - 3x^{2}}{3\\,y(x)^{2} - 9x} \\\\ \\\\\n\n\\displaystyle \\color{blue}{\\frac{dy}{dx}} &amp;\\color{blue}{=}&amp; \\color{blue}{\\dfrac{3\\,y(x) - x^{2}}{y(x)^{2} - 3x}}\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u308c\u3092\u7528\u3044\u308c\u3070\u3001\u66f2\u7dda\u4e0a\u306e\u3042\u308b\u70b9\u304c\u5206\u304b\u3063\u3066\u3044\u308b\u3068\u304d\u3001\u305d\u306e\u70b9\u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u50be\u304d\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30b0\u30e9\u30d5\u304b\u3089\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(2,4)<\/span><\/span> \u304c\u66f2\u7dda\u4e0a\u306b\u3042\u308b\u3068\u63a8\u6e2c\u3067\u304d\u307e\u3059\u3002\u5b9f\u969b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2^3 + 4^3 - 9\\cdot 2\\cdot 4 = 8+64 - 72 = 0<\/span><\/span> \u306a\u306e\u3067\u78ba\u304b\u306b\u66f2\u7dda\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u77e5\u308c\u3070\u3001\u305d\u306e\u70b9\u3092\u901a\u308b\u63a5\u7dda\u306e\u50be\u304d\u306f\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\left.\\frac{dy}{dx}\\right|_{(2,4)}= \\frac{3\\cdot 4 - 2^2}{4^2 - 3\\cdot 2}= \\frac{8}{10}= \\frac{4}{5}}<\/span>\n<p><a name=\"221\"><\/a><\/p>\n<h4>\u6709\u7406\u3079\u304d\u306e\u5c0e\u95a2\u6570<\/h4>\n<p>\u9670\u95a2\u6570\u5fae\u5206\u3092\u4f7f\u3048\u3070\u3001\u57fa\u672c\u7684\u306a\u5fae\u5206\u6280\u6cd5\u306e\u4e00\u3064\u3067\u3042\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=x^n<\/span><\/span>\uff08\u305f\u3060\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\in\\mathbb{Z}<\/span><\/span>\uff09\u3092\u6709\u7406\u6570\u306b\u307e\u3067\u62e1\u5f35\u3067\u304d\u3001\u6b21\u306e\u516c\u5f0f\u304c\u5bb9\u6613\u306b\u5c0e\u304b\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}x^{p\/q}= \\frac{p}{q}x^{(p\/q) -1}<\/span>\n<p>\u3053\u3053\u3067\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p,q\\in\\mathbb{Z}<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q\\neq 0<\/span><\/span> \u3067\u3059\u3002<\/p>\n<p>\u3053\u308c\u3092\u793a\u3059\u306b\u306f\u3001\u307e\u305a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=x^{p\/q}<\/span><\/span> \u3068\u7f6e\u304d\u3001\u81ea\u7136\u5bfe\u6570\u3092\u3068\u308c\u3070\uff1a<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(y) = \\displaystyle \\frac{p}{q}\\ln(x)<\/span>\n<p>\u6b21\u306b\u3001\u3053\u306e\u5f0f\u3092\u9670\u5fae\u5206\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle \\frac{1}{y}\\frac{dy}{dx} = \\frac{p}{q}\\frac{1}{x}<\/span>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\color{blue}{\\frac{dy}{dx} = \\frac{p}{q}\\frac{1}{x}y(x)= \\frac{p}{q}\\frac{1}{x}x^{p\/q} = \\frac{p}{q}x^{(p\/q) - 1}}<\/span><\/span><\/p>\n<p><a name=\"3\"><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KwJ5Bb5Ch_o\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/a><\/p>\n<h2>\u6f14\u7fd2\u554f\u984c\u96c6\uff1a<\/h2>\n<h4>1 \u5909\u6570\u306e\u9023\u9396\u6cd5\u5247<\/h4>\n<ol>\n<li>\u6b21\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u3088\uff1a<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"20px\">a.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=(x^2-3)^{12}<\/span><\/span><\/td>\n<td width=\"20px\">b.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\displaystyle \\left(\\frac{4x^3 - x\\cos(2x) - 1}{\\sin(2x) + 2} \\right)^5<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"20px\">c.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\cos(1-x^2)<\/span><\/span><\/td>\n<td width=\"20px\">d.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\tan(x\\cos(3-x^2))<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"20px\">e.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\displaystyle \\frac{1}{(\\sec(2x)-1)^{3\/2}}<\/span><\/span><\/td>\n<td width=\"20px\">f.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\displaystyle \\frac{\\tan(2x)}{1-\\cot(2x)}<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"20px\">g.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\displaystyle \\ln\\left(\\frac{\\tan(x)}{x^2+1}\\right)<\/span><\/span><\/td>\n<td width=\"20px\">h.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=3^{\\csc(4x)}<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\u6b21\u306e\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u3088\uff1a<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"20px\">a.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\displaystyle \\frac{1}{\\sqrt{x}arctan\\left(x^3\\right)}<\/span><\/span><\/td>\n<td width=\"20px\">b.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\displaystyle \\frac{{arcsec}(x^2-x+2)}{\\sqrt{x^2+1}}<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"20px\">c.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=x^x<\/span><\/span><\/td>\n<td width=\"20px\">d.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)={arccsc}\\left(x^{\\ln(x)}\\right)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"20px\">e.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)=\\ln\\left(arctan(e^x)\\right)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u95a2\u6570\u5408\u6210\u306e\u5c0e\u95a2\u6570\u306b\u5bfe\u3059\u308b\u9023\u9396\u6cd5\u5247 \u3053\u3053\u307e\u3067\u306b\u5b66\u3093\u3067\u304d\u305f\u5185\u5bb9\u306b\u3088\u308a\u3001\u307b\u3068\u3093\u3069\u3042\u3089\u3086\u308b\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u57fa\u672c\u7684\u306a\u9053\u5177\u306f\u3059\u3067\u306b\u305d\u308d\u3063\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3042\u308b\u5c0e\u95a2\u6570\u3092\u300c\u8a08\u7b97\u3067\u304d\u308b\u300d\u3053\u3068\u3068\u3001\u305d\u306e\u8a08\u7b97\u3092\u5b9f\u969b\u306b\u884c\u3046\u969b\u306b\u5fc5\u8981\u3068\u306a\u308b\u52b4\u529b\u3068\u306f\u533a\u5225\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u305d\u3057\u3066\u3001\u307e\u3055\u306b\u3053\u306e\u70b9\u306b\u304a\u3044\u3066\u30011 \u5909\u6570\u306e\u5834\u5408\u306e\u9023\u9396\u6cd5\u5247\u306a\u3069\u306e\u5b9a\u7406\u304c\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u9023\u9396\u6cd5\u5247\u3092\u7528\u3044\u308c\u3070\u3001\u672c\u6765\u3067\u3042\u308c\u3070\u304b\u306a\u308a\u7169\u96d1\u3067\u9762\u5012\u306a\u8a08\u7b97\u3092\u8981\u3059\u308b\u5c0e\u95a2\u6570\u3092\u3001\u8fc5\u901f\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 \u76ee\u6b21 \u5b9f\u6570\u5024 1 \u5909\u6570\u306b\u304a\u3051\u308b\u9023\u9396\u6cd5\u5247\u306e\u5b9a\u7406 \u9023\u9396\u6cd5\u5247\u306e\u8a3c\u660e \u4e00\u5909\u6570\u95a2\u6570\u306b\u304a\u3051\u308b\u9023\u9396\u6cd5\u5247\u306e\u5229\u7528\u4f8b \u9023\u9396\u6cd5\u5247\u3092\u7528\u3044\u308b\u969b\u306b\u7559\u610f\u3059\u3079\u304d\u70b9 \u9023\u9396\u6cd5\u5247\u304b\u3089\u5f97\u3089\u308c\u308b\u6709\u7528\u306a\u7d50\u679c \u9006\u95a2\u6570\u5b9a\u7406 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