{"id":34350,"date":"2024-11-27T12:00:17","date_gmt":"2024-11-27T12:00:17","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34350"},"modified":"2025-09-07T03:26:49","modified_gmt":"2025-09-07T03:26:49","slug":"%e9%96%a2%e6%95%b0%e3%81%ae%e6%a5%b5%e9%99%90%e3%81%a8%e3%81%97%e3%81%a6%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e9%96%a2%e6%95%b0%e3%81%ae%e6%a5%b5%e9%99%90%e3%81%a8%e3%81%97%e3%81%a6%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u95a2\u6570\u306e\u6975\u9650\u3068\u3057\u3066\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<style>\np{\ntext-align:justify;\n}\n<\/style>\n<h1 style=\"text-align:center;\">\u95a2\u6570\u306e\u6975\u9650\u3068\u3057\u3066\u306e\u5c0e\u95a2\u6570<\/h2>\n<p style=\"text-align:center;\"><em><strong>\u8981\u7d04:<\/strong><br \/>\n\u672c\u8b1b\u7fa9\u3067\u306f\u3001\u5c0e\u95a2\u6570\u3092\u95a2\u6570\u306e\u5909\u5316\u3092\u5206\u6790\u3059\u308b\u305f\u3081\u306e\u6570\u5b66\u7684\u624b\u6bb5\u3068\u3057\u3066\u63a2\u7a76\u3059\u308b\u3002\u5272\u7dda\u306e\u50be\u304d\u304b\u3089\u51fa\u767a\u3057\u3001\u70b9\u304c\u63a5\u8fd1\u3059\u308b\u6975\u9650\u3092\u53d6\u308b\u3053\u3068\u3067\u3001\u63a5\u7dda\u306e\u50be\u304d\u3068\u3057\u3066\u5c0e\u95a2\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u3002\u3055\u3089\u306b\u3001\u305d\u306e\u4e3b\u8981\u306a\u6027\u8cea\u3068\u898f\u5247\u3001\u3059\u306a\u308f\u3061\u548c\u3001\u7a4d\u3001\u5546\u306e\u898f\u5247\u3092\u5b66\u3073\u3001\u95a2\u6570\u3084\u5909\u5316\u306e\u73fe\u8c61\u306e\u5206\u6790\u306b\u304a\u3051\u308b\u5c0e\u95a2\u6570\u306e\u5fdc\u7528\u3092\u7406\u89e3\u3059\u308b\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u7fd2\u76ee\u6a19<\/strong><br \/>\n\u672c\u8b1b\u7fa9\u3092\u7d42\u3048\u305f\u5f8c\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b:\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>: \u5c0e\u95a2\u6570\u3092\u3001\u95a2\u6570\u306b\u304a\u3051\u308b\u77ac\u9593\u7684\u306a\u5909\u5316\u3092\u8a18\u8ff0\u3059\u308b\u6975\u9650\u3068\u3057\u3066\u3001\u307e\u305f\u3042\u308b\u70b9\u306b\u304a\u3051\u308b\u66f2\u7dda\u306e\u63a5\u7dda\u306e\u50be\u304d\u3068\u3057\u3066\u6349\u3048\u308b\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong>: \u5fae\u5206\u53ef\u80fd\u6027\u304c\u95a2\u6570\u306e\u9023\u7d9a\u6027\u3092\u610f\u5473\u3059\u308b\u3053\u3068\u3002<\/li>\n<li><strong>\u8a3c\u660e\u3059\u308b<\/strong>: \u5f62\u5f0f\u7684\u5b9a\u7fa9\u304b\u3089\u5c0e\u304b\u308c\u308b\u57fa\u672c\u7684\u306a\u5fae\u5206\u898f\u5247\u3002<\/li>\n<li><strong>\u5229\u7528\u3059\u308b<\/strong>: \u5c0e\u95a2\u6570\u306e\u4ee3\u6570\u7684\u6027\u8cea\uff08\u548c\u3001\u7a4d\u3001\u5546\uff09\u3092\u6570\u5b66\u7684\u554f\u984c\u306b\u9069\u7528\u3059\u308b\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u76ee\u6b21<\/u>:<\/strong><br \/>\n<a href=\"#1\"><strong>\u5c0e\u95a2\u6570\u306e\u6982\u5ff5<\/strong><\/a><br \/>\n<a href=\"#2\">\u5272\u7dda\u306e\u50be\u304d<\/a><br \/>\n<a href=\"#3\">\u6975\u9650\u3078\u306e\u79fb\u884c: \u5c0e\u95a2\u6570\u3068\u63a5\u7dda\u306e\u50be\u304d<\/a><br \/>\n<a href=\"#4\">\u5225\u306e\u5b9a\u7fa9<\/a><br \/>\n<a href=\"#5\"><strong>\u5c0e\u95a2\u6570\u306e\u6027\u8cea<\/strong><\/a><br \/>\n<a href=\"#6\">\u5fae\u5206\u53ef\u80fd\u6027\u306f\u9023\u7d9a\u6027\u3092\u610f\u5473\u3059\u308b<\/a><br \/>\n<a href=\"#\">\u5c0e\u95a2\u6570\u306e\u4ee3\u6570<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/TFxATgmYvkY\" 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>\u5c0e\u95a2\u6570\u306e\u6982\u5ff5<\/h2>\n<p>\u81ea\u7136\u754c\u306f\u4e00\u822c\u306b\u5909\u5316\u306b\u3055\u3089\u3055\u308c\u3084\u3059\u304f\u3001\u305d\u306e\u5909\u5316\u3092\u8a08\u7b97\u3057\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u6700\u3082\u512a\u308c\u305f\u6570\u5b66\u7684\u624b\u6bb5\u304c\u5c0e\u95a2\u6570\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u300c\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u306e\u5024\u306f\u5909\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x<\/span><\/span> \u306e\u3088\u3046\u306b\u4efb\u610f\u306b\u5c0f\u3055\u306a\u91cf\u3060\u3051\u5897\u6e1b\u3055\u305b\u305f\u3068\u304d\u306b\u3069\u3046\u306a\u308b\u304b?\u300d\u3068\u3044\u3046\u554f\u3044\u304b\u3089\u751f\u3058\u308b\u3002\u5c0e\u95a2\u6570\u306e\u6982\u5ff5\u306f\u3001\u3053\u306e\u554f\u3044\u3092\u5206\u6790\u3059\u308b\u4e2d\u3067\u95a2\u6570\u306e\u6975\u9650\u3068\u3057\u3066\u73fe\u308c\u308b\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u5272\u7dda\u306e\u50be\u304d<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=164s\" target=\"_blank\" rel=\"noopener\"><strong>\u95a2\u6570\u3092\u8003\u3048\u308b<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u30922\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 + \\Delta x<\/span><\/span> \u3067\u8a55\u4fa1\u3059\u308b\u3002\u66f2\u7dda\u306e2\u70b9\u3092\u901a\u308b\u3059\u3079\u3066\u306e\u76f4\u7dda\u306f\u300c\u5272\u7dda\u300d\u3068\u547c\u3070\u308c\u3001\u56f3\u306b\u793a\u3055\u308c\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/--KZ1YA55iug\/YI_jLiez_RI\/AAAAAAAAFCs\/xYcWyzwUaf88McAiTNK7l6tOSZQKyZFdwCLcBGAsYHQ\/s0\/graficosecante.PNG\" alt=\"\u5272\u7dda\u306e\u30b0\u30e9\u30d5\" class=\" aligncenter lazyload\" width=\"397\" height=\"233\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/--KZ1YA55iug\/YI_jLiez_RI\/AAAAAAAAFCs\/xYcWyzwUaf88McAiTNK7l6tOSZQKyZFdwCLcBGAsYHQ\/s0\/graficosecante.PNG\" alt=\"\u5272\u7dda\u306e\u30b0\u30e9\u30d5\" class=\" aligncenter lazyload\" width=\"397\" height=\"233\" \/><\/noscript><\/p>\n<p>\u3053\u306e\u7279\u5b9a\u306e\u5272\u7dda\u306e\u50be\u304d\u306f\u6b21\u306e\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\Delta f(x_0)}{\\Delta x} = \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u6975\u9650\u3078\u306e\u79fb\u884c: \u5c0e\u95a2\u6570\u3068\u63a5\u7dda\u306e\u50be\u304d<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=278s\" target=\"_blank\" rel=\"noopener\"><strong>\u66f2\u7dda\u306b\u5bfe\u3059\u308b\u5272\u7dda\u3092\u8003\u3048\u308b\u3068<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=f(x)<\/span><\/span>\u3001\u3053\u308c\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 + \\Delta x<\/span><\/span> \u3092\u901a\u308b\u3002\u3053\u306e\u3068\u304d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x<\/span><\/span> \u304c\u30bc\u30ed\u306b\u8fd1\u3065\u304f\u6975\u9650\u3092\u53d6\u308b\u3068\u3001\u5f97\u3089\u308c\u308b\u306e\u306f\u66f2\u7dda\u4e0a\u306e\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_0, f(x_0))<\/span><\/span> \u3092\u901a\u308b\u63a5\u7dda\u3067\u3042\u308b\u3002<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-8wCxY7adTBw\/YI_kfLeezzI\/AAAAAAAAFC0\/o6nKbRKv1SISYU3Rx7ML5Rly29edqey3ACLcBGAsYHQ\/s0\/grafico%2Brecta%2Btangente.PNG\" alt=\"\u63a5\u7dda\u306e\u30b0\u30e9\u30d5\" class=\" aligncenter lazyload\" width=\"464\" height=\"268\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-8wCxY7adTBw\/YI_kfLeezzI\/AAAAAAAAFC0\/o6nKbRKv1SISYU3Rx7ML5Rly29edqey3ACLcBGAsYHQ\/s0\/grafico%2Brecta%2Btangente.PNG\" alt=\"\u63a5\u7dda\u306e\u30b0\u30e9\u30d5\" class=\" aligncenter lazyload\" width=\"464\" height=\"268\" \/><\/noscript><\/p>\n<p>\u3053\u308c\u306b\u57fa\u3065\u304d\u3001\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u304a\u3051\u308b\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u306e\u5c0e\u95a2\u6570\u306e\u5f62\u5f0f\u7684\u5b9a\u7fa9\u304c\u6b21\u306e\u3088\u3046\u306b\u5c0e\u304b\u308c\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{df(x_0)}{dx}:= \\lim_{\\Delta x \\to 0}\\dfrac{\\Delta f(x_0)}{\\Delta x} = \\lim_{\\Delta x \\to 0} \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span><\/span><\/p>\n<p>\u3053\u308c\u306f\u540c\u6642\u306b\u3001\u70b9 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3092\u901a\u308b\u63a5\u7dda\u306e\u50be\u304d\u3092\u8868\u3057\u3066\u3044\u308b\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u5225\u306e\u5b9a\u7fa9<\/h3>\n<p>\u5c0e\u95a2\u6570\u3092\u6975\u9650\u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u5225\u306e\u65b9\u6cd5\u306f\u3001\u6b21\u306e\u7f6e\u63db\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nx_i &amp;= x_0\\\\\n\nx_f &amp;= x_i + \\Delta x\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u308c\u306b\u3088\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x = x_f - x_i<\/span><\/span> \u3068\u306a\u308a\u3001\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u306f\u6b21\u306e\u5f62\u306b\u306a\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\dfrac{df(x_i)}{dx} &amp;=\\displaystyle \\lim_{\\Delta x \\to 0}\\dfrac{ f(x_i + \\Delta x) - f(x_i)}{\\Delta x}\\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{x_f - x_i \\to 0} \\dfrac{f(x_f) - f(x_i)}{x_f - x_i}\\\\ \\\\\n\n&amp;=\\displaystyle  \\lim_{x_f \\to x_i } \\dfrac{f(x_f) - f(x_i)}{x_f - x_i}\n\n\\end{array}\n\n<\/span>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-GLyWOue8OUs\/YJAHOc_lTOI\/AAAAAAAAFC8\/3IV-onfsq9QC4nyweccS4ZN_O-JlWVz8wCLcBGAsYHQ\/s0\/definicion%2Bderivada%2Bcomo%2Blimite.PNG\" alt=\"\u5272\u7dda\u306e\u50be\u304d\u306e\u6975\u9650\u3068\u3057\u3066\u306e\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\" class=\" aligncenter lazyload\" width=\"469\" height=\"243\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-GLyWOue8OUs\/YJAHOc_lTOI\/AAAAAAAAFC8\/3IV-onfsq9QC4nyweccS4ZN_O-JlWVz8wCLcBGAsYHQ\/s0\/definicion%2Bderivada%2Bcomo%2Blimite.PNG\" alt=\"\u5272\u7dda\u306e\u50be\u304d\u306e\u6975\u9650\u3068\u3057\u3066\u306e\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\" class=\" aligncenter lazyload\" width=\"469\" height=\"243\" \/><\/noscript><\/p>\n<p>\u4e21\u65b9\u306e\u5b9a\u7fa9\u306f\u540c\u5024\u3067\u3042\u308a\u3001\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u4f7f\u3044\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u5c0e\u95a2\u6570\u306e\u6027\u8cea<\/h2>\n<p>\u95a2\u6570\u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u306b\u304a\u3044\u3066\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u3068\u306f\u3001\u6b21\u306e\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span><\/span><\/p>\n<p>\u307e\u305f\u3001\u533a\u9593 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u306e\u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in I<\/span><\/span> \u306b\u5bfe\u3057\u3066\u6975\u9650\u304c\u9069\u5207\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u306e\u95a2\u6570\u306f <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u4e0a\u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u3068\u8a00\u3046\u3002\u5fae\u5206\u53ef\u80fd\u306a\u95a2\u6570\u306b\u306f\u6b21\u306e\u3088\u3046\u306a\u6027\u8cea\u304c\u3042\u308b\u3002<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u5fae\u5206\u53ef\u80fd\u6027\u306f\u9023\u7d9a\u6027\u3092\u610f\u5473\u3059\u308b<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=526s\" target=\"_blank\" rel=\"noopener\"><strong>\u3082\u3057\u95a2\u6570\u304c <\/strong><\/a><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308c\u3070\u3001\u305d\u308c\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3067\u9023\u7d9a\u3067\u3042\u308b\u3002\u3053\u306e\u3053\u3068\u306f\u6b21\u306e\u8b70\u8ad6\u306b\u3088\u3063\u3066\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3067\u9023\u7d9a\u3067\u3042\u308b\u305f\u3081\u306b\u306f\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0}f(x) = f(x_0) <\/span><\/span><\/p>\n<p>\u3053\u306e\u5f0f\u306e\u5de6\u8fba\u3092\u8abf\u3079\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\lim_{x\\to x_0} f(x) &amp;= \\displaystyle \\lim_{x\\to x_0} \\left[ f(x) + f(x_0) - f(x_0) \\right] \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{x\\to x_0} \\left[f(x_0) + \\left( f(x)  - f(x_0) \\right) \\right] \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{x\\to x_0} \\left[f(x_0) + \\left( \\dfrac{f(x)  - f(x_0)}{x- x_0} \\right)(x-x_0)  \\right] \\\\ \\\\\n\n&amp;=f(x_0) +\\displaystyle \\lim_{x\\to x_0} \\left[ \\left( \\dfrac{f(x)  - f(x_0)}{x- x_0} \\right)(x-x_0) \\right] \\\\ \\\\\n\n\\end{array}\n\n<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3067\u9023\u7d9a\u3067\u3042\u308b\u305f\u3081\u306b\u306f\u3001\u53f3\u8fba\u306e\u6975\u9650\u304c\u9069\u5207\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u305d\u3057\u3066\u305d\u306e\u3088\u3046\u306a\u3053\u3068\u304c\u6210\u308a\u7acb\u3064\u306e\u306f\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u5834\u5408\u306b\u9650\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} \\dfrac{f(x) - f(x_0)}{x-x_0} =\\dfrac{df(x_0)}{dx}<\/span><\/span><\/p>\n<p>\u8a00\u3044\u63db\u3048\u308c\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u5834\u5408\u3067\u3042\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308c\u3070\u3001\u305d\u308c\u306f\u305d\u306e\u70b9\u3067\u9023\u7d9a\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u5c0e\u95a2\u6570\u306e\u4ee3\u6570<\/h3>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g<\/span><\/span> \u3092\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in I<\/span><\/span> \u4e0a\u3067\u5fae\u5206\u53ef\u80fd\u306a\u95a2\u6570\u3068\u3057\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta\\in\\mathbb{R}<\/span><\/span> \u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( \\alpha f(x) \\pm \\beta g(x) \\right) = \\alpha \\dfrac{df(x)}{dx} \\pm \\beta\\dfrac{dg(x)}{dx}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( f(x) g(x) \\right) = \\dfrac{df(x)}{dx}g(x) - f(x)\\dfrac{dg(x)}{dx}<\/span><\/span><\/li>\n<li>\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x)\\neq 0<\/span><\/span> \u306a\u3089\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( \\dfrac{f(x)}{g(x)} \\right) = \\dfrac{\\dfrac{df(x)}{dx}g(x) - f(x) \\dfrac{dg(x)}{dx} }{\\left[g(x)\\right]^2}<\/span><\/span><\/li>\n<\/ol>\n<p>\u898b\u3066\u306e\u3068\u304a\u308a\u3001\u5c0e\u95a2\u6570\u306e\u4ee3\u6570\u306f\u4e00\u898b\u3057\u305f\u307b\u3069\u76f4\u611f\u7684\u3067\u306f\u306a\u3044\u3002\u3057\u304b\u3057\u3001\u3053\u308c\u3089\u306e\u6027\u8cea\u306e\u8a3c\u660e\u306f\u3001\u6975\u9650\u3068\u3057\u3066\u306e\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u304b\u3089\u6bd4\u8f03\u7684\u5bb9\u6613\u306b\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p><span style=\"color: #000080;\">\u8a3c\u660e:<\/span><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=925s\" target=\"_blank\" rel=\"noopener\"><strong>\u548c\u306e\u5c0e\u95a2\u6570\u306e\u8a3c\u660e<\/strong><\/a> \u306f\u6b21\u306e\u63a8\u8ad6\u306b\u5f93\u3046\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left(\\alpha f(x) \\pm \\beta g(x) \\right) &amp; =\\displaystyle \\lim_{\\Delta x\\to 0} \\dfrac{\\left[\\alpha f(x+\\Delta x) \\pm \\beta g(x+ \\Delta x)\\right] - \\left[\\alpha f(x) \\pm \\beta g(x) \\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ \\left[\\alpha f(x+\\Delta x) - \\alpha f(x)\\right] \\pm \\left[\\beta g(x+\\Delta x) - \\beta g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ \\alpha \\left[ f(x+\\Delta x) -  f(x)\\right] \\pm  \\beta  \\left[ g(x+\\Delta x) - g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\alpha \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) -  f(x)}{\\Delta x} \\pm \\beta \\lim_{\\Delta x \\to 0} \\dfrac{ g(x+\\Delta x) -  g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\alpha \\dfrac{df(x)}{dx} \\pm \\beta \\dfrac{dg(x)}{dx}\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: center;\">\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=1059s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e00\u65b9\u3067\u3001\u7a4d\u306e\u5c0e\u95a2\u6570\u306e\u8a3c\u660e<\/strong><\/a> \u306f\u3084\u3084\u8907\u96d1\u3067\u3042\u308b\u304c\u3001\u305d\u308c\u307b\u3069\u96e3\u3057\u3044\u3082\u306e\u3067\u306f\u306a\u3044\u3002<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left[f(x)g(x)\\right] &amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) g(x+\\Delta x) -  f(x) g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) g(x+\\Delta x) + \\color{red}f(x)g(x+\\Delta x) - f(x)g(x+\\Delta x) \\color{black} - f(x) g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\left[f(x+\\Delta x) - f(x) \\right] g(x+\\Delta x) + f(x) \\left[g(x+\\Delta x)  - g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{\\Delta x \\to 0} g(x+\\Delta x) \\dfrac{f(x+\\Delta x) - f(x)}{\\Delta x} + f(x)\\lim_{\\Delta x \\to 0} \\dfrac{g(x+\\Delta x) - g(x)}{\\Delta x}\\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{\\Delta x \\to 0} g(x+\\Delta x)\\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) - f(x)}{\\Delta x} + f(x)\\lim_{\\Delta x \\to 0} \\dfrac{g(x+\\Delta x) - g(x)}{\\Delta x}\\\\ \\\\\n\n&amp;= g(x) \\dfrac{df(x)}{dx} + f(x)\\dfrac{dg(x)}{dx}\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u3053\u3067\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g<\/span><\/span> \u304c\u5fae\u5206\u53ef\u80fd\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u308c\u304c\u9023\u7d9a\u3067\u3042\u308a\u3001\u3057\u305f\u304c\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{\\Delta x\\to 0 } g(x+\\Delta x) = g(x)<\/span><\/span> \u3068\u306a\u308b\u4e8b\u5b9f\u3092\u5229\u7528\u3057\u3001\u305d\u306e\u5f8c<strong>\u6975\u9650\u306e\u4ee3\u6570<\/strong>\u3092\u7528\u3044\u3066\u8a3c\u660e\u3092\u7d50\u8ad6\u3065\u3051\u3066\u3044\u308b\u3002<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=162s\" target=\"_blank\" rel=\"noopener\"><strong>\u6700\u5f8c\u306b\u3001\u5546\u306e\u5c0e\u95a2\u6570\u306e\u8a3c\u660e\u306e\u305f\u3081\u306b<\/strong><\/a>\u3001\u7a4d\u306e\u5c0e\u95a2\u6570\u306e\u7d50\u679c\u3092\u5229\u7528\u3067\u304d\u308b\u3002\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k(x) = f(x)\/g(x)<\/span><\/span> \u3092\u8003\u3048\u3001\u305f\u3060\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x)\\neq 0<\/span><\/span> \u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u6b21\u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\dfrac{df(x)}{dx}= \\dfrac{d}{dx}(k(x)g(x)) = \\dfrac{dk(x)}{dx}g(x) + k(x)\\dfrac{dg(x)}{dx}<\/span><\/span><\/p>\n<p>\u3053\u3053\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{dk(x)}{dx}<\/span><\/span> \u3092\u89e3\u304f\u3068\u3001\u6b21\u3092\u5f97\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{dk(x)}{dx}g(x) = \\dfrac{df(x)}{dx} - k(x)\\dfrac{dg(x)}{dx} = \\dfrac{d}{dx}f(x) - \\dfrac{f(x)}{g(x)}\\dfrac{dg(x)}{dx} <\/span><\/span><\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left(\\dfrac{f(x)}{g(x)}\\right)\n\n &amp;= \\dfrac{dk(x)}{dx} =\\dfrac{1}{g(x)} \\dfrac{df(x)}{dx} - \\dfrac{f(x)}{\\left[g(x)\\right]^2}\\dfrac{dg(x)}{dx} \\\\ \\\\\n\n&amp; = \\dfrac{\\dfrac{df(x)}{dx}g(x) - f(x) \\dfrac{dg(x)}{dx}}{[g(x)]^2}\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u308c\u306f\u307e\u3055\u306b\u793a\u3057\u305f\u304b\u3063\u305f\u3082\u306e\u3067\u3042\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u95a2\u6570\u306e\u6975\u9650\u3068\u3057\u3066\u306e\u5c0e\u95a2\u6570 \u8981\u7d04: \u672c\u8b1b\u7fa9\u3067\u306f\u3001\u5c0e\u95a2\u6570\u3092\u95a2\u6570\u306e\u5909\u5316\u3092\u5206\u6790\u3059\u308b\u305f\u3081\u306e\u6570\u5b66\u7684\u624b\u6bb5\u3068\u3057\u3066\u63a2\u7a76\u3059\u308b\u3002\u5272\u7dda\u306e\u50be\u304d\u304b\u3089\u51fa\u767a\u3057\u3001\u70b9\u304c\u63a5\u8fd1\u3059\u308b\u6975\u9650\u3092\u53d6\u308b\u3053\u3068\u3067\u3001\u63a5\u7dda\u306e\u50be\u304d\u3068\u3057\u3066\u5c0e\u95a2\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u3002\u3055\u3089\u306b\u3001\u305d\u306e\u4e3b\u8981\u306a\u6027\u8cea\u3068\u898f\u5247\u3001\u3059\u306a\u308f\u3061\u548c\u3001\u7a4d\u3001\u5546\u306e\u898f\u5247\u3092\u5b66\u3073\u3001\u95a2\u6570\u3084\u5909\u5316\u306e\u73fe\u8c61\u306e\u5206\u6790\u306b\u304a\u3051\u308b\u5c0e\u95a2\u6570\u306e\u5fdc\u7528\u3092\u7406\u89e3\u3059\u308b\u3002 \u5b66\u7fd2\u76ee\u6a19 \u672c\u8b1b\u7fa9\u3092\u7d42\u3048\u305f\u5f8c\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b: 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