{"id":2327,"date":"2022-02-25T17:50:50","date_gmt":"2022-02-25T08:50:50","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2327"},"modified":"2025-06-09T12:08:01","modified_gmt":"2025-06-09T03:08:01","slug":"%e9%99%b0%e9%96%a2%e6%95%b0%e5%ae%9a%e7%90%86","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\/%e9%99%b0%e9%96%a2%e6%95%b0%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u9670\u95a2\u6570\u5b9a\u7406"},"content":{"rendered":"

2\u5909\u6570\u95a2\u6570\u306e\u504f\u5fae\u5206\u306e\u5fdc\u7528\u3068\u3057\u3066\uff0c\u9670\u95a2\u6570\u5b9a\u7406\u3092\u7d39\u4ecb\u3059\u308b\u3002
\n\\(f(x, y) =0\\) \u3092\u6e80\u305f\u3059\u9670\u95a2\u6570 \\(y = y(x)\\) \u306e\u5fae\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002
\n$$ \\frac{dy}{dx} = – \\frac{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial x}\\ \\ }{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial y}\\ \\ }, \\quad \\frac{\\partial f}{\\partial y} \\neq 0$$
\n<\/p>\n

\n

\u967d\u95a2\u6570\uff0c\u9670\u95a2\u6570<\/h3>\n

\\(z = f(x, y)\\) \u306b\u304a\u3044\u3066\uff0c\\(f(x, y) = 0\\) \u3068\u3044\u3046\u6761\u4ef6\u3092\u3064\u3051\u308b\u3068\uff0c2\u3064\u306e\u5909\u6570 \\(x, y\\) \u306f\u72ec\u7acb\u3067\u306f\u306a\u304f\uff0c\\(x\\) \u306e\u5024\u3092\u4e0e\u3048\u308b\u3068\uff0c\\(y\\) \u306e\u5024\u304c\u6c7a\u307e\u3063\u3066\u3057\u307e\u3046\u3002\u3064\u307e\u308a\uff0c\\(y\\) \u306f \\(x\\) \u306e\u95a2\u6570\u3068\u306a\u308b\uff1a
\n$$ f(x, y) = 0 \\quad\\Rightarrow\\quad y = y(x)$$<\/p>\n

\u5b9f\u969b\u306b\uff0c\\(f(x, y) = 0\\) \u304b\u3089\uff0c\\(y = y(x)\\) \u3068\u3042\u304b\u3089\u3055\u307e\u306b\u89e3\u3051\u308b\u306e\u3067\u3042\u308c\u3070\uff0c\u300c\\(y\\) \u306f \\(x\\) \u306e\u967d\u95a2\u6570<\/b><\/span>\u3067\u66f8\u3051\u308b\u300d\u3068\u3044\u3046\u3002\u305f\u3068\u3048\uff0c\\(y = y(x)\\) \u3068\u3042\u304b\u3089\u3055\u307e\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u306a\u304f\u3066\u3082\uff0c\\(f(x,y) = 0\\) \u3068\u3044\u3046\u6761\u4ef6\u306b\u3088\u3063\u3066\uff0c \\(y\\) \u306f \\(x\\) \u306e\u95a2\u6570\u3067\u3042\u308b\u3053\u3068\u306f\u308f\u304b\u308b\u3002\u3053\u306e\u3068\u304d\uff0c\\(y=y(x)\\) \u3092 \\(f(x, y) = \\) \u3092\u6e80\u305f\u3059\u300c\u9670\u95a2\u6570<\/b><\/span>\u300d\u3068\u3044\u3046\u3002
\n\u3064\u307e\u308a\uff0c$$ f(x, y(x)) = 0$$<\/p>\n

\u9670\u95a2\u6570\u306e\u5fae\u5206\uff1a\u9670\u95a2\u6570\u5b9a\u7406<\/h3>\n

\\(f(x, y) =0\\) \u3092\u6e80\u305f\u3059\u9670\u95a2\u6570 \\(y = y(x)\\) \u306e\u5fae\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002
\n$$ \\frac{dy}{dx} = – \\frac{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial x}\\ \\ }{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial y}\\ \\ }, \\quad \\frac{\\partial f}{\\partial y} \\neq 0$$<\/p>\n

\u8a3c\u660e<\/h4>\n

\\( f(x, y) = f(x, y(x)) = 0 \\) \u3092\\(x\\) \u3067\u5fae\u5206\u3057\u3066 $$ \\frac{df}{dx} = \\frac{\\partial f}{\\partial x}\\frac{dx}{dx} + \\frac{\\partial f}{\\partial y} \\frac{dy}{dx} = \\frac{\\partial f}{\\partial x} + \\frac{\\partial f}{\\partial y} \\frac{dy}{dx} = 0$$<\/p>\n

$$\\therefore\\ \\ \\frac{dy}{dx} = – \\frac{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial x}\\ \\ }{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial y}\\ \\ }$$<\/p>\n","protected":false},"excerpt":{"rendered":"

2\u5909\u6570\u95a2\u6570\u306e\u504f\u5fae\u5206\u306e\u5fdc\u7528\u3068\u3057\u3066\uff0c\u9670\u95a2\u6570\u5b9a\u7406\u3092\u7d39\u4ecb\u3059\u308b\u3002 \\(f(x, y) =0\\) \u3092\u6e80\u305f\u3059\u9670\u95a2\u6570 \\(y = y(x)\\) \u306e\u5fae\u5206\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002 $$ \\frac{dy}{dx} = – \\frac{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial x}\\ \\ }{\\displaystyle \\ \\ \\frac{\\partial f}{\\partial y}\\ \\ }, \\quad \\frac{\\partial f}{\\partial y} \\neq 0$$<\/p>

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2226,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2327","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\/2327","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=2327"}],"version-history":[{"count":6,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2327\/revisions"}],"predecessor-version":[{"id":10467,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2327\/revisions\/10467"}],"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=2327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}