{"id":362,"date":"2019-10-13T11:34:56","date_gmt":"2019-10-13T03:34:56","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=362"},"modified":"2025-02-26T11:10:38","modified_gmt":"2025-02-26T03:10:38","slug":"gradient","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2019\/10\/13\/gradient\/","title":{"rendered":"\u4e3a\u4ec0\u4e48\u68af\u5ea6\u65b9\u5411\u4e0e\u5916\u6cd5\u7ebf\u65b9\u5411\u4e00\u81f4\uff1f"},"content":{"rendered":"<p><script type=\"text\/javascript\" async src=\"https:\/\/www.caiqinyi.cn\/wp-content\/MathJax\/MathJax.js?config=TeX-AMS_CHTML\">\n<\/script><br \/>\n<script type=\"text\/x-mathjax-config\">\n    MathJax.Hub.Config({\n        tex2jax: {inlineMath: [['$','$']]},\n        TeX: {equationNumbers: {autoNumber: [\"AMS\"], useLabelIds: true}},\n        \"HTML-CSS\": {linebreaks: {automatic: true}},\n        SVG: {linebreaks: {automatic: true}}\n    });\n<\/script><\/p>\n<p>\u6570\u5206\u7684\u4e1c\u897f\u90fd\u5fd8\u4e86\u4e0d\u5c11\u2026\u2026 \u6765\u8865\u8865\u8bfe, \u5728\u6c42\u4e00\u4e9b\u6709\u89e3\u6790\u5f62\u5f0f\u7684\u66f2\u7ebf\u6cd5\u5411\u7684\u65f6\u5019\u5f88\u6709\u7528~<\/p>\n<p><!--more--><\/p>\n<p><strong>\u53c2\u8003\u6750\u6599<\/strong><br \/>\n1. <a href=\"https:\/\/zhuanlan.zhihu.com\/p\/27731819\">\u4e3a\u4ec0\u4e48\u68af\u5ea6\u7684\u65b9\u5411\u4e0e\u7b49\u9ad8\u7ebf\u5207\u7ebf\u65b9\u5411\u5782\u76f4\uff1f<\/a><\/p>\n<p>\u4e0d\u59a8\u5047\u8bbe\u66f2\u7ebf\u65b9\u7a0b\u4e3a$z=f(x,y)$, \u8be5\u66f2\u9762\u88ab\u5e73\u9762$z=c$\u622a\u53d6\u5f97\u5230\u7684\u66f2\u7ebf\u65b9\u7a0b\u4e3a<\/p>\n<p>$$z=f(x,y), \\\\ z=c.$$<\/p>\n<p>\u800c\u8fd9\u6761\u66f2\u7ebf\u5728$XOY$\u5e73\u9762\u4e0a\u7684\u6295\u5f71\u4e3a\u5e73\u9762\u66f2\u7ebf$Q:f(x,y)=c$, \u5e76\u79f0\u5176\u4e3a\u66f2\u7ebf$z=f(x,y)$\u7684\u7b49\u9ad8\u7ebf.<\/p>\n<p>\u7531\u4e8e\u7b49\u9ad8\u7ebf$f(x,y)=c$\u4e0a\u4efb\u610f\u4e00\u70b9\u7684\u5207\u7ebf\u659c\u7387\u4e3a$dy\/dx=-f_x\/f_y$(\u9690\u51fd\u6570\u5b58\u5728\u5b9a\u7406), \u6545\u5176\u6cd5\u7ebf\u659c\u7387\u4e3a$f_y\/f_x$. \u53c8\u68af\u5ea6\u4e3a$(f_x,f_y)$, \u5176\u65b9\u5411\u4e3a$f_y\/f_x$, \u7531\u6b64\u53ef\u4ee5\u770b\u51fa\u68af\u5ea6\u7684\u65b9\u5411\u4e0e\u7b49\u9ad8\u7ebf$f(x,y)=c$\u4e0a\u4efb\u4e00\u4e00\u70b9\u7684\u5916\u6cd5\u7ebf\u65b9\u5411\u662f\u76f8\u540c\u7684. \u8fd9\u4e5f\u5c31\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48\u68af\u5ea6\u7684\u65b9\u5411\u4e0e\u7b49\u9ad8\u7ebf\u5207\u7ebf\u65b9\u5411\u5782\u76f4\u7684\u539f\u56e0.<\/p>\n<p>\u7ed3\u8bba\u5982\u4e0b: \u51fd\u6570$z=f(x,y)$\u5728\u70b9$(x,y)$\u7684\u68af\u5ea6\u65b9\u5411\u4e0e\u8fc7\u70b9$(x,y)$\u7684\u7b49\u9ad8\u7ebf$f(x,y)=c$\u5728\u8be5\u70b9\u7684\u6cd5\u7ebf\u65b9\u5411\u76f8\u540c. \u68af\u5ea6\u7684\u65b9\u5411\u4e0e\u7b49\u9ad8\u7ebf\u5207\u7ebf\u65b9\u5411\u5782\u76f4.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u5206\u7684\u4e1c\u897f\u90fd\u5fd8\u4e86\u4e0d\u5c11\u2026\u2026 \u6765\u8865\u8865\u8bfe, \u5728\u6c42\u4e00\u4e9b\u6709\u89e3\u6790\u5f62\u5f0f\u7684\u66f2\u7ebf\u6cd5\u5411\u7684\u65f6\u5019\u5f88\u6709\u7528~<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/362"}],"collection":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/comments?post=362"}],"version-history":[{"count":16,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/362\/revisions"}],"predecessor-version":[{"id":3617,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/362\/revisions\/3617"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}