{"id":5158,"date":"2022-03-07T18:42:21","date_gmt":"2022-03-07T09:42:21","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=5158"},"modified":"2022-07-20T14:14:23","modified_gmt":"2022-07-20T05:14:23","slug":"differential-2","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/differential-2.html","title":{"rendered":"\u5fae\u5206\u4fc2\u6570\u30fb\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3068\u6570\u5b66\u3067\u5fae\u5206\u3092\u3059\u308b\u516c\u5f0f\u306e\u6027\u8cea"},"content":{"rendered":"\n<p>\u63a5\u7dda\u306e\u50be\u304d\u3092\u77e5\u308a\u305f\u3044\u3068\u304d\u3001\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u65b0\u305f\u306a\u95a2\u6570\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5fae\u5206\u3068\u3044\u3046\u306e\u306f\u3001\u63a5\u7dda\u306e\u50be\u304d\u3092\u5f97\u308b\u305f\u3081\u306e\u64cd\u4f5c\u3067\u3059\u3002<\/p>\n<p>\u5fae\u5206\u3092\u5b66\u3076\u3068\u304d\u3001\u5c0e\u95a2\u6570\u3068\u5fae\u5206\u4fc2\u6570\u3092\u7fd2\u3044\u307e\u3059\u3002\u5fae\u5206\u4fc2\u6570\u3068\u306f\u3001\u63a5\u7dda\u306e\u50be\u304d\u3092\u6307\u3057\u307e\u3059\u3002\u307e\u305f\u5c0e\u95a2\u6570\u3068\u306f\u3001\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u65b0\u305f\u306a\u95a2\u6570\u3092\u6307\u3057\u307e\u3059\u3002\u5fae\u5206\u3059\u308b\u3068\u3001\u5fc5\u305a\u5c0e\u95a2\u6570\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u5c0e\u95a2\u6570\u3092\u51fa\u305b\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u307e\u305f\u3001\u5fae\u5206\u306e\u516c\u5f0f\u3092\u3069\u306e\u3088\u3046\u306b\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u9ad8\u6821\u6570\u5b66\u306e\u5fae\u5206\u30fb\u7a4d\u5206\u3067\u306f\u3001\u5148\u306b\u5fae\u5206\u3092\u7fd2\u3044\u307e\u3059\u3002\u5fae\u5206\u306e\u521d\u6b69\u306f\u5185\u5bb9\u304c\u96e3\u3057\u304f\u306a\u304f\u3001\u3069\u306e\u3088\u3046\u306b\u5fae\u5206\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u50be\u304d\u3092\u5f97\u3089\u308c\u308b\u5f0f\u3092\u4f5c\u308b\u306e\u304c\u5fae\u5206<\/h2>\n<p>\u5fae\u5206\u3068\u306f\u3001\u4f55\u3092\u610f\u5473\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u6570\u5b66\u3067\u306e\u5fae\u5206\u3068\u306f\u3001\u63a5\u7dda\u306e\u50be\u304d\u3092\u5f97\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/p>\n<p>\u50be\u304d\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\\(x\\)\u306e\u5909\u5316\u91cf\u3068\\(y\\)\u306e\u5909\u5316\u91cf\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\\(y=x^2\\)\u306e\u95a2\u6570\u306b\u3064\u3044\u3066\u3001\\((1,1)\\)\u3068\\((3,9)\\)\u3092\u7d50\u3076\u76f4\u7dda\u306e\u50be\u304d\u306f\u3044\u304f\u3089\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/rey6.jpg\" alt=\"\" width=\"400\" height=\"407\" class=\"aligncenter size-full wp-image-5164\" \/><\/p>\n<p>\\(x\\)\u304c2\u5897\u3048\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\\(y\\)\u306f8\u5897\u3048\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u30812\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u306e\u50be\u304d\u306f4\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{8}{2}=4\\)<\/li>\n<\/ul>\n<p>\u5fae\u5206\u3092\u7406\u89e3\u3059\u308b\u3068\u304d\u3001\u300c2\u70b9\u306e\\(x\\)\u306e\u5909\u5316\u91cf\u3068\\(y\\)\u306e\u5909\u5316\u91cf\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u3067\u50be\u304d\u3092\u5f97\u3089\u308c\u308b\u300d\u3053\u3068\u3092\u307e\u305a\u306f\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u6975\u9650\u5024\u3092\u5229\u7528\u3057\u3001\u9650\u308a\u306a\u304f0\u306b\u8fd1\u3065\u3051\u308b\u3053\u3068\u3067\u5fae\u5206\u4fc2\u6570\u3092\u5f97\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u6587\u5b57\u3092\u5229\u7528\u3057\u3066\u50be\u304d\u3092\u8868\u3057\u307e\u3057\u3087\u3046\u3002\u5ea7\u6a19A\u306b\u3064\u3044\u3066\u3001\u53f3\u306bh\u79fb\u52d5\u3059\u308b\u5834\u5408\u3001\u50be\u304d\u306f\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u5ea7\u6a19A\u306b\u3064\u3044\u3066\u3001\\(x\\)\u5ea7\u6a19\u304c\\(a\\)\u306e\u3068\u304d\u3001\\(y\\)\u5ea7\u6a19\u306f\\(f(a)\\)\uff08\\(x\\)\u306b\\(a\\)\u306e\u5024\u3092\u4ee3\u5165\u3057\u305f\u5024\uff09\u3067\u3059\u3002\u6b21\u306b\u3001\u5ea7\u6a19A\u304b\u3089\u53f3\u306bh\u79fb\u52d5\u3057\u305f\u5ea7\u6a19B\u3092\u8003\u3048\u307e\u3059\u3002\u5ea7\u6a19B\u306e\\(x\\)\u5ea7\u6a19\u306f\\(a+h\\)\u3067\u3059\u3002\u307e\u305f\u70b9B\u306e\\(y\\)\u5ea7\u6a19\u306f\\(f(a+h)\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u50be\u304d\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{f(a+h)-f(a)}{(a+h)-a}=\\displaystyle\\frac{f(a+h)-f(a)}{h}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/rku1.jpg\" alt=\"\" width=\"600\" height=\"277\" class=\"aligncenter size-full wp-image-5180\" \/><\/p>\n<p>\u305f\u30602\u70b9\u3092\u7d50\u3076\u5834\u5408\u3001\u305d\u308c\u306f\u63a5\u7dda\u306e\u50be\u304d\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u63a5\u7dda\u306e\u50be\u304d\u3092\u5f97\u308b\u306b\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u5148\u307b\u3069\u3001\u5ea7\u6a19A\u304b\u3089\u53f3\u306bh\u9032\u3093\u3060\u70b9\u3092\u5ea7\u6a19B\u306b\u3057\u307e\u3057\u305f\u3002\u305d\u308c\u3067\u306f\u3001h\u306e\u8ddd\u96e2\u30920.00000001\u306e\u3088\u3046\u306b\u975e\u5e38\u306b\u5c0f\u3055\u3044\u5024\u306b\u3059\u308c\u3070\u3069\u3046\u3067\u3057\u3087\u3046\u304b\u3002\u3053\u306e\u5834\u5408\u3001<span style=\"color: #0000ff;\">\u300c2\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u306e\u50be\u304d\u3067\u306f\u3042\u308b\u3082\u306e\u306e\u3001\u5b9f\u8cea\u7684\u306b\u4e00\u3064\u306e\u70b9\u306e\u63a5\u7dda\u3092\u8868\u3057\u3066\u3044\u308b\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p>\\(h\\)\u306e\u5024\u30920\u306b\u8fd1\u3065\u3051\u308b\u5834\u5408\u3001\u6570\u5b66\u3067\u306f\\(\\displaystyle \\lim_{ h \\to 0 }\\)\u3068\u8868\u73fe\u3057\u307e\u3059\u3002\u305d\u3053\u3067\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{f(a+h)-f(a)}{h}\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u5f0f\u306f\u300c\u5ea7\u6a19A\\((a,f(a))\\)\u3068\u5ea7\u6a19B\\((a+h,f(a+h))\\)\u3092\u7d50\u3076\u76f4\u7dda\u306e\u50be\u304d\u306b\u3064\u3044\u3066\u3001h\u306e\u5024\u3092\u6975\u9650\u307e\u30670\u306b\u3059\u308b\u300d\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u3001\\(f(x)=x^2\\)\u306e\u95a2\u6570\u306e\u5834\u5408\u306f\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u5ea7\u6a19A\u306f\\((a,a^2)\\)\u3068\u306a\u308a\u3001\u5ea7\u6a19B\u3067\u306f\\((a+h,(a+h)^2)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u4ee3\u5165\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{f(a+h)-f(a)}{h}\\)<\/p>\n<p>\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n<p>\\(\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{(a+h)^2-a^2}{h}\\)<\/p>\n<p>\\(\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{(a^2+2ah+h^2)-a^2}{h}\\)<\/p>\n<p>\\(\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{2ah+h^2}{h}\\)<\/p>\n<p>\\(\\displaystyle \\lim_{ h \\to 0 }2a+h\\)<\/p>\n<p>\u307e\u305f<span style=\"color: #ff0000;\">\\(\\displaystyle \\lim_{ h \\to 0 }\\)\u3068\u3044\u3046\u306e\u306f\u3001\\(h\u22520\\)\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/span>h\u3092\u7121\u8996\u3067\u304d\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle \\lim_{ h \\to 0 }2a+h=2a\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\\(x\\)\u5ea7\u6a19\u304c\\(a\\)\u306e\u3068\u304d\u3001\u50be\u304d\u306f\\(2a\\)\u306b\u306a\u308b\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\\(x\\)\u5ea7\u6a19\u304c3\u306e\u3068\u304d\u3001\u50be\u304d\u306f6\u3067\u3059\u3002\u307e\u305f\\(x\\)\u5ea7\u6a19\u304c4\u306e\u3068\u304d\u3001\u50be\u304d\u306f8\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u63a5\u7dda\u306e\u50be\u304d\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3068\u304d\u5f97\u3089\u308c\u308b\u63a5\u7dda\u306e\u50be\u304d\u3092\u5fae\u5206\u4fc2\u6570\u3068\u3044\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\\(x=3\\)\u306e\u3068\u304d\u306e\u5fae\u5206\u4fc2\u6570\u306f6\u3067\u3059\u3002\\(x=4\\)\u306e\u3068\u304d\u306e\u5fae\u5206\u4fc2\u6570\u306f8\u3067\u3059\u3002<\/p>\n<h3>\u5c0e\u95a2\u6570\u3092\u5229\u7528\u3057\u3001\u63a5\u7dda\u306e\u50be\u304d\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u5fae\u5206\u4fc2\u6570\u3092\u5b66\u3079\u3070\u3001\u5c0e\u95a2\u6570\u3092\u7406\u89e3\u3067\u304d\u307e\u3059\u3002\u5fae\u5206\u4fc2\u6570\u3082\u5c0e\u95a2\u6570\u3082\u307b\u307c\u540c\u3058\u6982\u5ff5\u3060\u304b\u3089\u3067\u3059\u3002\u5148\u307b\u3069\u3001\u5ea7\u6a19A\\((a,f(a))\\)\u3067\u306e\u5ea7\u6a19\u3092\u8003\u3048\u307e\u3057\u305f\u3002\u305d\u3053\u3067\\(x\\)\u5ea7\u6a19\u3092\\(a\\)\u3067\u306f\u306a\u304f\u3001\\(x\\)\u306b\u7f6e\u304d\u63db\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u3046\u3059\u308b\u3068\u3001\\(a\\)\u304c\\(x\\)\u306b\u7f6e\u304d\u63db\u308f\u3063\u305f\u5148\u307b\u3069\u3068\u540c\u3058\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{f(x+h)-f(x)}{(x+h)-x}=\\displaystyle\\frac{f(x+h)-f(x)}{h}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/rku2.jpg\" alt=\"\" width=\"600\" height=\"285\" class=\"aligncenter size-full wp-image-5181\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u5c0e\u304d\u51fa\u3055\u308c\u308b\u65b0\u305f\u306a\u95a2\u6570\u3092\u5c0e\u95a2\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\\(f(x)=x^2\\)\u306e\u5c0e\u95a2\u6570\u306f\\(f'(x)=2x\\)\u3067\u3059\u3002\u306a\u304a\\(f'(x)\\)\u3068\u306f\u3001\\(f(x)\\)\u3092\u5fae\u5206\u3057\u305f\u95a2\u6570\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u5148\u307b\u3069\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u306b\u3088\u3063\u3066\\(f(x)=x^2\\)\u306e\u5c0e\u95a2\u6570\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(f'(x)=\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{f(x+h)-f(x)}{h}\\)<\/p>\n<p>\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n<p>\\(f'(x)=\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{(x+h)^2-x^2}{h}\\)<\/p>\n<p>\\(f'(x)=\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{(x^2+2hx+h^2)-x^2}{h}\\)<\/p>\n<p>\\(f'(x)=\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{2hx+h^2}{h}\\)<\/p>\n<p>\\(f'(x)=\\displaystyle \\lim_{ h \\to 0 }2x+h\\)<\/p>\n<p>\\(f'(x)=2x\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u5f97\u3089\u308c\u305f\u65b0\u305f\u306a\u95a2\u6570\\(f'(x)=2x\\)\u304c\u5c0e\u95a2\u6570\u3067\u3059\u3002\\(f(x)=x^2\\)\u3092\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\\(f'(x)=2x\\)\u3092\u5f97\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\u524d\u8ff0\u306e\u901a\u308a\u3001\\(x=3\\)\u306e\u3068\u304d\u306e\u5fae\u5206\u4fc2\u6570\uff08\u50be\u304d\uff09\u306f6\u3067\u3059\u3002\\(x=4\\)\u306e\u3068\u304d\u306e\u5fae\u5206\u4fc2\u6570\uff08\u50be\u304d\uff09\u306f8\u3067\u3059\u3002<span style=\"color: #0000ff;\">\u5fae\u5206\u4fc2\u6570\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u306f\u3001\u5c0e\u95a2\u6570\u3092\u5f97\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/span>\u3044\u305a\u308c\u306b\u3057\u3066\u3082\u3001\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u63a5\u7dda\u306e\u50be\u304d\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<h3>\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u3066\u5fae\u5206\u3059\u308b<\/h3>\n<p>\u306a\u304a\u5fae\u5206\u3059\u308b\u3068\u304d\u3001\u554f\u984c\u306b\u3088\u3063\u3066\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u3066\u5fae\u5206\u3059\u308b\u3088\u3046\u306b\u554f\u308f\u308c\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u3066\u5fae\u5206\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u4f8b\u3048\u3070\u4ee5\u4e0b\u306e\u95a2\u6570\u306b\u3064\u3044\u3066\u3001\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u3066\u5fae\u5206\u3059\u308b\u3068\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(y=x^2-2x\\)<\/li>\n<\/ul>\n<p>\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(y&#8217;=\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{(x+h)^2-2(x+h)-(x^2-2x)}{h}\\)<\/p>\n<p>\\(y&#8217;=\\displaystyle \\lim_{ h \\to 0 }\\displaystyle\\frac{2hx+h^2-2h}{h}\\)<\/p>\n<p>\\(y&#8217;=\\displaystyle \\lim_{ h \\to 0 }2x+h-2\\)<\/p>\n<p>\\(y&#8217;=2x-2\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3001\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b<\/h2>\n<p>\u305f\u3060\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u3068\u304d\u3001\u5b9a\u7fa9\u3092\u5229\u7528\u3057\u3066\u5fae\u5206\u3059\u308b\u3053\u3068\u306f\u307b\u3068\u3093\u3069\u3042\u308a\u307e\u305b\u3093\u3002\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u3001\u95a2\u6570\u3092\u5fae\u5206\u3057\u307e\u3059\u3002<\/p>\n<p>\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\\(f(x)=x^n\\)\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f'(x)=nx^{n-1}\\)<\/li>\n<\/ul>\n<p>\u4f8b\u3048\u3070\\(f(x)=x^3\\)\u3092\u5fae\u5206\u3059\u308b\u5834\u5408\u3001\\(f'(x)=3x^2\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/rku3.jpg\" alt=\"\" width=\"313\" height=\"211\" class=\"aligncenter size-full wp-image-5166\" \/><\/p>\n<p>\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3092\u5229\u7528\u3059\u308b\u3088\u308a\u3082\u3001\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u307b\u3046\u304c\u7c21\u5358\u306b\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(f(x)=1\\)\u3092\u5fae\u5206\uff1a\\(f'(x)=0\\)<\/li>\n<li>\\(f(x)=x\\)\u3092\u5fae\u5206\uff1a\\(f'(x)=1\\)<\/li>\n<li>\\(f(x)=x^2\\)\u3092\u5fae\u5206\uff1a\\(f'(x)=2x\\)<\/li>\n<li>\\(f(x)=x^3\\)\u3092\u5fae\u5206\uff1a\\(f'(x)=3x^2\\)<\/li>\n<li>\\(f(x)=x^4\\)\u3092\u5fae\u5206\uff1a\\(f'(x)=4x^3\\)<\/li>\n<\/ul>\n<p>\u5fae\u5206\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u3053\u306e\u3088\u3046\u306b\u5c0e\u95a2\u6570\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u5c0e\u95a2\u6570\u306e\u6027\u8cea\u3092\u7406\u89e3\u3057\u3001\u63a5\u7dda\u3092\u5f97\u3089\u308c\u308b\u5f0f\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u306a\u304a\u5b9f\u969b\u306b\u5fae\u5206\u3059\u308b\u3068\u304d\u3001\u3088\u308a\u8907\u96d1\u306a\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u5c0e\u95a2\u6570\u306e\u6027\u8cea\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\\(a\\)\u3068\\(b\\)\u3092\u5b9a\u6570\u3068\u3059\u308b\u3068\u304d\u3001\u5c0e\u95a2\u6570\u306b\u306f\u4ee5\u4e0b\u306e\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\{a\u00d7f(x)\\}&#8217;=a\u00d7f'(x)\\)<\/li>\n<\/ul>\n<p>\u4f8b\u3048\u3070\\(f(x)=3x^2\\)\u3092\u5fae\u5206\u3059\u308b\u5834\u5408\u3001\\(f'(x)\\)\\(=3\u00d72x=6x\\)\u306b\u306a\u308a\u307e\u3059\u3002\\(f(x)\\)\\(=-4x^3\\)\u3092\u5fae\u5206\u3059\u308b\u5834\u5408\u3001\\(f'(x)\\)\\(=-4\u00d73x^2\\)\\(=-12x^2\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\{f(x)+g(x)\\}&#8217;=f'(x)+g'(x)\\)<\/li>\n<\/ul>\n<p>\u4f8b\u3048\u3070\\(y=x^3+x^2\\)\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u3001\\(x^3\\)\u3068\\(x^2\\)\u3092\u305d\u308c\u305e\u308c\u5fae\u5206\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u5c0e\u95a2\u6570\u306f\\(y&#8217;\\)\\(=3x^2+2x\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\{af(x)+bg(x)\\}&#8217;=af'(x)+bg'(x)\\)<\/li>\n<\/ul>\n<p>\u4f8b\u3048\u3070\\(y=2x^3+3x+2\\)\u3092\u5fae\u5206\u3059\u308b\u3068\u304d\u3001\\(2x^3\\)\u3068\\(3x\\)\u3068\\(2\\)\u3092\u305d\u308c\u305e\u308c\u5fae\u5206\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u5c0e\u95a2\u6570\u306f\\(y&#8217;\\)\\(=6x^2+3\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u95a2\u6570\u3092\u5fae\u5206\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u516c\u5f0f\u3092\u899a\u3048\u308c\u3070\u3001\u7c21\u5358\u306b\u5c0e\u95a2\u6570\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<h3>\u5c0e\u95a2\u6570\u3092\u5229\u7528\u3057\u3066\u95a2\u6570\u3092\u6c42\u3081\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u767a\u5c55\u7684\u306a\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(f'(1)=f'(-1)=1\\),\\(f(1)=0\\),\\(f(-1)=2\\)\u306e\u3068\u304d\u3001\u3053\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u4e09\u6b21\u95a2\u6570\\(f(x)\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\(f(x)\\)\u306f\u4e09\u6b21\u95a2\u6570\u306a\u306e\u3067\u3001\\(f(x)\\)\\(=ax^3\\)\\(+bx^2\\)\\(+cx+d\\)\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u5fae\u5206\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(f'(x)=3ax^2+2bx+c\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(f'(1)=3a+2b+c=1\\)<\/p>\n<p>\\(f'(-1)=3a-2b+c=1\\)<\/p>\n<p>\u6b21\u306b\\(f'(1)-f'(-1)\\)\u3092\u3059\u308b\u3068\u3001\\(4b=0\\)\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(b=0\\)\u3067\u3059\u3002\\(b=0\\)\u306a\u306e\u3067\u3001\\(f(x)=ax^3+cx+d\\)\u3068\u8868\u305b\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\\(f(1)=0\\),\\(f(-1)=2\\)\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(f(1)=a+c+d=0\\)<\/p>\n<p>\\(f(-1)=-a-c+d=2\\)<\/p>\n<p>\\(f(1)+f(-1)\\)\u3092\u3059\u308b\u3068\u3001\\(2d=2\\)\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(d=1\\)\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\\(f(1)=a+c+1=0\\)\u3088\u308a\u3001\\(c=-a-1\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(f'(1)=3a+c=1\\)\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(3a+(-a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