{"id":2308,"date":"2022-02-25T17:18:55","date_gmt":"2022-02-25T08:18:55","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2308"},"modified":"2024-07-11T09:34:54","modified_gmt":"2024-07-11T00:34:54","slug":"%e5%81%8f%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/%e5%81%8f%e5%be%ae%e5%88%86%ef%bc%9a%e5%a4%9a%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%81%8f%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u504f\u5c0e\u95a2\u6570"},"content":{"rendered":"

2\u5909\u6570\u95a2\u6570 \\( z = f(x, y) \\) \u306e\u504f\u5fae\u5206 \\(\\displaystyle \\frac{\\partial f}{\\partial x}, \\ \\frac{\\partial f}{\\partial y} \\) \u306e\u5b9a\u7fa9\u306e\u307e\u3068\u3081\u3002<\/p>\n

<\/p>\n

\n

\u504f\u5fae\u5206\u306e\u5b9a\u7fa9<\/h3>\n

1\u5909\u6570\u95a2\u6570 \\( y = f(x) \\) \u306e\u5fae\u5206 \\(\\displaystyle \\frac{df}{dx}\\) \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u3066\u3044\u305f\u306e\u3067\u3042\u3063\u305f\u3002<\/p>\n

$$ \\frac{dy}{dx} = \\frac{df}{dx} \\equiv \\lim_{\\Delta x \\rightarrow 0}\\frac{f(x+\\Delta x) -f(x)}{\\Delta x}$$<\/p>\n

\u540c\u69d8\u306b\u3057\u3066\uff0c2\u5909\u6570\u95a2\u6570 \\(z = f(x, y) \\) \u306e \\(x\\)-\u504f\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\uff08\u3064\u307e\u308a\uff0c \\(x\\) \u3067\u504f\u5fae\u5206\u3059\u308b\uff09\u3068\u306f\uff0c\\(x\\) \u4ee5\u5916\u306e\u5909\u6570\u3092\u3042\u305f\u304b\u3082\u5b9a\u6570\u3067\u3042\u308b\u3068\u3057\u3066 \\(x\\) \u306e\u307f\u3092\\(\\Delta x\\) \u3060\u3051\u5fae\u5c0f\u5909\u5316\u3055\u305b\u305f\u5897\u52a0\u7387\u306e\u6975\u9650\u3067\u3042\u308a\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n

$$\\frac{\\partial z}{\\partial x} = \\frac{\\partial f}{\\partial x} \\equiv \\lim_{\\Delta x \\rightarrow 0} \\frac{f(x + \\Delta x, y)\u00a0 -f(x, y)}{\\Delta x} $$<\/p>\n

\u307e\u305f\uff0c2\u5909\u6570\u95a2\u6570 \\(z = f(x, y) \\) \u306e \\(y\\)-\u504f\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u308b\uff08\u3064\u307e\u308a\uff0c \\(y\\) \u3067\u504f\u5fae\u5206\u3059\u308b\uff09\u3068\u306f\uff0c\\(y\\) \u4ee5\u5916\u306e\u5909\u6570\u3092\u3042\u305f\u304b\u3082\u5b9a\u6570\u3067\u3042\u308b\u3068\u3057\u3066 \\(y\\) \u306e\u307f\u3092\\(\\Delta y\\) \u3060\u3051\u5fae\u5c0f\u5909\u5316\u3055\u305b\u305f\u5897\u52a0\u7387\u306e\u6975\u9650\u3067\u3042\u308a\uff0c<\/p>\n

$$\\frac{\\partial z}{\\partial y} = \\frac{\\partial f}{\\partial y} \\equiv \\lim_{\\Delta y \\rightarrow 0} \\frac{f(x , y+ \\Delta y) -f(x, y)}{\\Delta y} $$<\/p>\n

\u504f\u5fae\u5206\u8a18\u53f7\u306e\u8aad\u307f\u65b9<\/h3>\n

\\(\\partial\\) \u306e\u8aad\u307f\u65b9\u306b\u3064\u3044\u3066\u306f\uff0c\u65e5\u672c\u8a9e\u5909\u63db\u30b7\u30b9\u30c6\u30e0\u7684\u306b\u306f\u300c\u3067\u308b\u300d\u3068\u304b\u300c\u3089\u3046\u3093\u3069\u3067\u3043\u30fc\u300d\u3068\u304b\u66f8\u3044\u3066\u5909\u63db\u3057\u3066\u3084\u308c\u3070\u51fa\u3066\u304f\u308b\u3002<\/p>\n

\\( \\displaystyle \\frac{\\partial f}{\\partial x} \\) \u306e\u8aad\u307f\u65b9\u306f\uff0c\u5404\u8005\u305d\u308c\u305e\u308c\u306e\u8a00\u3044\u56de\u3057\u304c\u3042\u308b\u3068\u601d\u3046\u304c\uff0c\u4f8b\u3048\u3070\u79c1\u306e\u96a3\u306e\u90e8\u5c4b\u306b\u3044\u308b I \u5148\u751f\u306b\u306a\u3089\u3046\u3068<\/p>\n

\u300c\u30c7\u30eb \u30a8\u30d5 \u30c7\u30eb \u30a8\u30c3\u30af\u30b9\u300d<\/p>\n

\u3053\u308c\u304c\u4e00\u756a\u8aad\u307f\u3084\u3059\u3044\u3002\u4ed6\u306b\u300c\u30e9\u30a6\u30f3\u30c9\u30c7\u30a3\u30fc \u30a8\u30d5 \u30e9\u30a6\u30f3\u30c9\u30c7\u30a3\u30fc \u30a8\u30c3\u30af\u30b9\u300d\u3068\u8aad\u3081\u306a\u3044\u3053\u3068\u3082\u306a\u3044\u304c\uff0c\u9577\u304f\u3066\u820c\u3092\u304b\u307f\u305d\u3046\u306a\u306e\u3067\uff0c\u300c\u30c7\u30a3\u30fc\u300d\u306e\u90e8\u5206\u3092\u7701\u7565\u3057\u3066\u300c\u30e9\u30a6\u30f3\u30c9 \u30a8\u30d5 \u30e9\u30a6\u30f3\u30c9 \u30a8\u30c3\u30af\u30b9\u300d\u3068\u8aad\u3080\u5834\u5408\u3082\u3042\u308b\u3002<\/p>\n

\u53c2\u8003\u307e\u3067\u306b\uff0c \\(\\LaTeX \\) \u8868\u8a18\u3067\u306f<\/p>\n

\\frac{\\partial f}{\\partial x}<\/pre>\n
\u3068\u66f8\u304f\u306e\u3067\uff0c\u300c\u30d1\u30fc\u30b7\u30e3\u30eb \u30a8\u30d5 \u30d1\u30fc\u30b7\u30e3\u30eb \u30a8\u30c3\u30af\u30b9\u300d\u3068\u8aad\u3080\u4eba\u3082\u307e\u308c\u306b\u3044\u308b\u304b\u3082\u77e5\u308c\u306a\u3044\u3002<\/p>\n
\u304f\u3069\u3044\u3088\u3046\u3060\u3051\u3069\uff0c1\u5909\u6570\u95a2\u6570\u306e\u5fae\u5206 \\(\\displaystyle \\frac{dy}{dx}\\) \u306f\u9ad8\u6821\u3067\u300c\u30c7\u30a3\u30fc \u30ef\u30a4 \u30c7\u30a3\u30fc \u30a8\u30c3\u30af\u30b9\u300d\u3068\u8aad\u307f\uff0c\u5206\u6570\u307f\u305f\u3044\u306b\u300c\u30c7\u30a3\u30fc \u30a8\u30c3\u30af\u30b9 \u3076\u3093\u306e \u30c7\u30a3\u30fc \u30ef\u30a4\u300d\u3068\u306f\u8aad\u307e\u306a\u3044\uff0c\u3068\u7fd2\u3063\u305f\u3068\u601d\u3044\u307e\u3059\u3002\u504f\u5fae\u5206\u3082\u540c\u69d8\u306b\u300c\u5206\u5b50\u300d\uff08\u6a2a\u68d2\u306e\u4e0a\u306e\u90e8\u5206\uff09\u304b\u3089\u8aad\u3093\u3067\u3044\u304d\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
2\u5909\u6570\u95a2\u6570 \\( z = f(x, y) \\) \u306e\u504f\u5fae\u5206 \\(\\displaystyle \\frac{\\partial f}{\\partial x}, \\ \\frac{\\partial f}{\\partial y} \\) \u306e\u5b9a\u7fa9\u306e\u307e\u3068\u3081\u3002<\/p>
\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2226,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2308","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2308","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=2308"}],"version-history":[{"count":5,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2308\/revisions"}],"predecessor-version":[{"id":9202,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2308\/revisions\/9202"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2226"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2308"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}