{"id":4397,"date":"2013-12-18T06:00:00","date_gmt":"2013-12-17T21:00:00","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4397"},"modified":"2014-09-10T16:49:10","modified_gmt":"2014-09-10T07:49:10","slug":"post-4397","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4397","title":{"rendered":"\u504f\u5fae\u5206"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000x \u304a\u3088\u3073 y \u306b\u5bfe\u3057\u3066\u306e <img src='https:\/\/s0.wp.com\/latex.php?latex=f%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='f(x, y)' title='f(x, y)' class='latex' \/> \u306e\u504f\u5c0e\u95a2\u6570\u306f\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+++%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+x%7D%3D+%5Clim%5Climits_%7Bh+%5Crightarrow+0%7D+%5Cfrac%7Bf%28x+%2B+h%2C+y%29+-+f%28x%2C+y%29%7D%7Bh%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+y%7D+%3D+%5Clim%5Climits_%7Bk+%5Crightarrow+0%7D+%5Cfrac%7Bf%28x%2C+y+%2B+k%29+-+f%28x%2C+y%29%7D%7Bk%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle   \\frac{\\partial f}{\\partial x}= \\lim\\limits_{h \\rightarrow 0} \\frac{f(x + h, y) - f(x, y)}{h}\\\\\\vspace{0.2 in}   \\frac{\\partial f}{\\partial y} = \\lim\\limits_{k \\rightarrow 0} \\frac{f(x, y + k) - f(x, y)}{k}' title='\\displaystyle   \\frac{\\partial f}{\\partial x}= \\lim\\limits_{h \\rightarrow 0} \\frac{f(x + h, y) - f(x, y)}{h}\\\\\\vspace{0.2 in}   \\frac{\\partial f}{\\partial y} = \\lim\\limits_{k \\rightarrow 0} \\frac{f(x, y + k) - f(x, y)}{k}' class='latex' \/><\/p>\n<p>\u3000\u3057\u3070\u3057\u3070 h = &Delta;x, k = &Delta;y \u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0ey \u3092\u5b9a\u6570\u3068\u3057\u305f x \u306b\u5bfe\u3059\u308b f \u306e\u901a\u5e38\u306e\u5c0e\u95a2\u6570\u306f\u5358\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cpartial+f%2F%5Cpartial+x&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\partial f\/\\partial x' title='\\partial f\/\\partial x' class='latex' \/> \u3068\u8a18\u8ff0\u3057\uff0c\u4e00\u65b9 x \u3092\u5b9a\u6570\u3068\u3057\u305f y \u306b\u5bfe\u3059\u308b f \u306e\u901a\u5e38\u306e\u5c0e\u95a2\u6570\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cpartial+f%2F%5Cpartial+y&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\partial f\/\\partial y' title='\\partial f\/\\partial y' class='latex' \/> \u3068\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n<p>\u3000\u9ad8\u968e\u306e\u5c0e\u95a2\u6570\u3082\u307e\u305f\u540c\u69d8\u306b\u5b9a\u7fa9\u3057\u307e\u3059\uff0e\u4f8b\u3048\u3070\uff0c2 \u968e\u306e\u901a\u5e38\u306e\u5c0e\u95a2\u6570\u306f\u4e0b\u8a18\u306e\u3088\u3046\u3067\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle++++%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D%5Cleft%28%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+x%7D%5Cright%29+%3D+%5Cfrac%7B%5Cpartial%5E2f%7D%7B%5Cpartial+x%5E2%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D%5Cleft%28%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+y%7D%5Cright%29+%3D+%5Cfrac%7B%5Cpartial%5E2f%7D%7B%5Cpartial+x%5Cpartial+y%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D%5Cleft%28%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+x%7D%5Cright%29+%3D+%5Cfrac%7B%5Cpartial%5E2f%7D%7B%5Cpartial+y%5Cpartial+x%7D%5C%5C%5Cvspace%7B0.2+in%7D+++%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D%5Cleft%28%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+y%7D%5Cright%29+%3D+%5Cfrac%7B%5Cpartial%5E2f%7D%7B%5Cpartial+y%5E2%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle    \\frac{\\partial}{\\partial x}\\left(\\frac{\\partial f}{\\partial x}\\right) = \\frac{\\partial^2f}{\\partial x^2}\\\\\\vspace{0.2 in}   \\frac{\\partial}{\\partial x}\\left(\\frac{\\partial f}{\\partial y}\\right) = \\frac{\\partial^2f}{\\partial x\\partial y}\\\\\\vspace{0.2 in}   \\frac{\\partial}{\\partial y}\\left(\\frac{\\partial f}{\\partial x}\\right) = \\frac{\\partial^2f}{\\partial y\\partial x}\\\\\\vspace{0.2 in}   \\frac{\\partial}{\\partial y}\\left(\\frac{\\partial f}{\\partial y}\\right) = \\frac{\\partial^2f}{\\partial y^2}' title='\\displaystyle    \\frac{\\partial}{\\partial x}\\left(\\frac{\\partial f}{\\partial x}\\right) = \\frac{\\partial^2f}{\\partial x^2}\\\\\\vspace{0.2 in}   \\frac{\\partial}{\\partial x}\\left(\\frac{\\partial f}{\\partial y}\\right) = \\frac{\\partial^2f}{\\partial x\\partial y}\\\\\\vspace{0.2 in}   \\frac{\\partial}{\\partial y}\\left(\\frac{\\partial f}{\\partial x}\\right) = \\frac{\\partial^2f}{\\partial y\\partial x}\\\\\\vspace{0.2 in}   \\frac{\\partial}{\\partial y}\\left(\\frac{\\partial f}{\\partial y}\\right) = \\frac{\\partial^2f}{\\partial y^2}' class='latex' \/><\/p>\n<p>\u3000\u504f\u5c0e\u95a2\u6570\u306f\u6642\u3005 f<sub>x<\/sub> \u3084 f<sub>y<\/sub> \u3068\u3082\u8a18\u8ff0\u3057\u307e\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408 f<sub>x<\/sub>(a, b), f<sub>y<\/sub>(a, b) \u306f\u70b9 (a, b) \u306b\u304a\u3044\u3066\u8a55\u4fa1\u3055\u308c\u308b\u3053\u308c\u3089\u306e\u504f\u5fae\u5206\u3067\u3059\uff0e<\/p>\n<p>\u3000\u504f\u5c0e\u95a2\u6570\u306f\u307e\u305f  f<sub>xx<\/sub>, f<sub>xy<\/sub>, f<sub>yx<\/sub>, f<sub>yy<\/sub> \u3068\u3082\u8a18\u8ff0\u3057\u307e\u3059\uff0ef \u304c\u5c11\u306a\u304f\u3068\u3082 2 \u968e\u306e\u9023\u7d9a\u306a\u504f\u5fae\u5206\u3092\u6709\u3059\u308b\u306a\u3089 2 \u968e\u3084 3 \u968e\u5fae\u5206\u306e\u7d50\u679c\u3082\u307e\u305f\u540c\u69d8\u3067\u3059\uff0e<\/p>\n<p>\u3000<img src='https:\/\/s0.wp.com\/latex.php?latex=f%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='f(x, y)' title='f(x, y)' class='latex' \/> \u306e\u5168\u5fae\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+df+%3D+%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+x%7Ddx+%2B+%5Cfrac%7B%5Cpartial+f%7D%7B%5Cpartial+y%7Ddy&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle df = \\frac{\\partial f}{\\partial x}dx + \\frac{\\partial f}{\\partial y}dy' title='\\displaystyle df = \\frac{\\partial f}{\\partial x}dx + \\frac{\\partial f}{\\partial y}dy' class='latex' \/><\/p>\n<p>\u3000\u305f\u3060\u3057 h = &Delta;x = dx, k = &Delta;y = dy \u3067\u3059\uff0e<\/p>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0071635408\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000x \u304a\u3088\u3073 y \u306b\u5bfe\u3057\u3066\u306e \u306e\u504f\u5c0e\u95a2\u6570\u306f\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e \u3000\u3057\u3070\u3057\u3070 h = &Delta;x, k = &Delta;y \u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0ey \u3092\u5b9a\u6570\u3068\u3057\u305f x \u306b\u5bfe\u3059\u308b f \u306e\u901a\u5e38\u306e\u5c0e\u95a2\u6570\u306f\u5358\u306b \u3068\u8a18\u8ff0\u3057\uff0c\u4e00 &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4397\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u504f\u5fae\u5206&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4397","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4397"}],"version-history":[{"count":10,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4397\/revisions"}],"predecessor-version":[{"id":6804,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4397\/revisions\/6804"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}