{"id":37,"date":"2023-09-17T11:00:07","date_gmt":"2023-09-17T11:00:07","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%b4%be%e7%94%9f%e8%a7%84%e5%88%99%e9%93%be\/"},"modified":"2023-09-17T11:00:07","modified_gmt":"2023-09-17T11:00:07","slug":"%e6%b4%be%e7%94%9f%e8%a7%84%e5%88%99%e9%93%be","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%b4%be%e7%94%9f%e8%a7%84%e5%88%99%e9%93%be\/","title":{"rendered":"\u94fe\u5f0f\u6cd5\u5219\uff08\u5bfc\u6570\uff09"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u94fe\u5f0f\u6cd5\u5219\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bfc\u51fa\u51fd\u6570\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u89e3\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u751a\u81f3\u53ef\u4ee5\u7ec3\u4e60\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u7684\u5bfc\u6570\u7684\u5206\u6b65\u6c42\u89e3\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-regla-de-la-cadena\"><\/span>\u4ec0\u4e48\u662f\u94fe\u5f0f\u6cd5\u5219\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u94fe\u5f0f\u6cd5\u5219\u662f\u7528\u4e8e\u63a8\u5bfc\u590d\u5408\u51fd\u6570\u7684\u516c\u5f0f\u3002<\/strong>\u94fe\u5f0f\u6cd5\u5219\u6307\u51fa\u590d\u5408\u51fd\u6570<em>f(g(x))<\/em>\u7684\u5bfc\u6570\u7b49\u4e8e\u5bfc\u6570<em>f'(g(x))<\/em>\u4e58\u4ee5\u5bfc\u6570<em>g'(x)<\/em> \u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/regle-de-la-chaine.webp\" alt=\"\u94fe\u5f0f\u6cd5\u5219\" class=\"wp-image-2207\" width=\"269\" height=\"269\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u89c1\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u51fd\u6570\u7684\u590d\u5408-\u590d\u5408\u51fd\u6570\/\">\u590d\u5408\u51fd\u6570<\/a><\/span><\/p>\n<p>\u975e\u6b63\u5f0f\u5730\uff0c\u94fe\u5f0f\u6cd5\u5219\u901a\u5e38\u88ab\u8ba4\u4e3a\u662f\u5bf9<em>\u51fd\u6570\u8fdb\u884c\u5fae\u5206\uff0c\u7136\u540e\u5c06\u5176\u4e58\u4ee5\u51fd\u6570\u4e2d\u7684\u503c<\/em>\u3002<\/p>\n<p>\u94fe\u5f0f\u6cd5\u5219\u516c\u5f0f\u4f7f\u6211\u4eec\u80fd\u591f\u66f4\u8f7b\u677e\u5730\u5fae\u5206\u590d\u5408\u51fd\u6570\uff0c\u56e0\u4e3a\u5982\u679c\u6211\u4eec\u8981\u4f7f\u7528\u5bfc\u6570\u5b9a\u4e49\u7684\u6781\u9650\u6765\u5fae\u5206\u51fd\u6570\u7684\u7ec4\u5408\uff0c\u6211\u4eec\u5c06\u4e0d\u5f97\u4e0d\u8fdb\u884c\u5927\u91cf\u8ba1\u7b97\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5fc5\u987b\u8003\u8651\u5230\u8be5\u89c4\u5219\u4ec5\u7528\u4e8e\u6c42\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u800c\u4e0d\u7528\u4e8e\u6c42\u4efb\u4f55\u7c7b\u578b\u7684\u51fd\u6570\u6216\u51fd\u6570\u8fd0\u7b97\u7684\u5bfc\u6570\u3002\u4f8b\u5982\uff0c\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\u9519\u8bef\u662f\u9519\u8bef\u5730\u5c06\u94fe\u5f0f\u6cd5\u5219\u5e94\u7528\u5230\u529f\u80fd\u6027\u4ea7\u54c1\u4e2d\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-de22604d9af306981b71d39bd190df75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x)\\cdot x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"68\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u274c<\/p>\n<p>\u4ec5<strong>\u5f53\u4e00\u4e2a\u51fd\u6570\u5305\u542b\u5728\u53e6\u4e00\u4e2a\u51fd\u6570\u4e2d\u65f6\uff0c<\/strong>\u624d\u80fd\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea93fb0bbc6f1ac5c2e26f2c5730627f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"45\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u2705 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-con-la-regla-de-la-cadena\"><\/span>\u5177\u6709\u94fe\u5f0f\u6cd5\u5219\u7684\u5bfc\u6570\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u51fa\u4e86\u94fe\u5f0f\u6cd5\u5219\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u5c06\u4ee5\u94fe\u5f0f\u6cd5\u5219\u4e3a\u4f8b\u63a8\u5bfc\u51fa\u51e0\u4e2a\u51fd\u6570\u3002\u8bf7\u8bb0\u4f4f\uff0c\u5982\u679c\u5728\u793a\u4f8b\u4e2d\u60a8\u4e0d\u660e\u767d\u5982\u4f55\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bfc\u51fa\u51fd\u6570\uff0c\u60a8\u53ef\u4ee5\u5728\u8bc4\u8bba\u4e2d\u8be2\u95ee\u6211\u4eec\uff01<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b1<\/h3>\n<p>\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bfc\u51fa x \u5e73\u65b9\u7684\u81ea\u7136\u5bf9\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-056e8e809ecf361f98a9ab4a6509e1a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u81ea\u7136\u5bf9\u6570\u7684\u5bfc\u6570\u7b49\u4e8e\u5176\u81ea\u53d8\u91cf\u7684 1 \u500d\uff0c\u56e0\u6b64\u5bfc\u6570<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4537be7e40864f78dd4bf5a5cdfb53ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'\\bigl(g(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"62\" style=\"vertical-align: -7px;\"><\/p>\n<p>\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82f88b45158f1890a0e60b2496a1898e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"331\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b66cdf74d9a89d4259495d799042e18c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\ln(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\cfrac{1}{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"396\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0cx \u7684 2 \u6b21\u65b9\u5bfc\u6570\u4e3a 2x\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0f0a7b2d096f09aacc349fe800f5ae6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u8ba1\u7b97\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\u3002\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\u5c06\u662f\u6211\u4eec\u521a\u521a\u627e\u5230\u7684\u4e24\u4e2a\u5bfc\u6570\u7684\u4e58\u79ef\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ad6b9a4a227664b616ffeef61781e54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x^2}\\cdot 2x = \\cfrac{2x}{x^2}=\\cfrac{2}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"458\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> \u5b9e\u65bd\u4f8b2<\/h3>\n<p>\u5728\u7b2c\u4e8c\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u57fa\u4e8e\u591a\u9879\u5f0f\u5bfc\u51fa\u52bf\u51fd\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1fd64daeb147f4af91e5eb8518621081_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^2+4x-5\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"179\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u5bfc\u51fa\u5e42\uff0c\u6211\u4eec\u9700\u8981\u5c06\u539f\u59cb\u6307\u6570\u653e\u5728\u5b83\u7684\u524d\u9762\uff0c\u5e76\u4ece\u6307\u6570\u4e2d\u51cf\u53bb\u4e00\u4e2a\u5355\u4f4d\uff0c\u56e0\u6b64\u4e0d\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u7684\u52bf\u51fd\u6570\u7684\u5bfc\u6570\u5c06\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9d0e7fc8a11cbd2103465a57128a9db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\left(3x^2+4x-5\\right)^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=3\\left(3x^2+4x-5\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"582\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u63a8\u5bfc\u62ec\u53f7\u91cc\u7684\u5185\u5bb9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dad3522b805cdb0c38e771bc6e630f50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=3x^2+4x-5\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=6x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"424\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u6c42\u89e3\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u8fd9\u5c06\u662f\u4e4b\u524d\u8ba1\u7b97\u7684\u4e24\u4e2a\u5bfc\u6570\u7684\u4e58\u79ef\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d4d80ad509263a9791efd441621d183_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^2+4x-5\\right)^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=3\\left(3x^2+4x-5\\right)^2\\cdot (6x+4)\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"582\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b3<\/h3>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u6c42\u89e3 x \u7684\u4e09\u6b21\u65b9\u52a0\u4e0a 7x \u7684\u6b63\u5f26\u5bfc\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42b994d7e38385bd61050cc50428beeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3+7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"154\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u662f\u4e00\u4e2a\u51fd\u6570\u7684\u590d\u5408\uff0c\u56e0\u4e3a\u6211\u4eec\u5728\u6b63\u5f26\u51fd\u6570\u4e2d\u6709\u51fd\u6570 x <sup>3<\/sup> +7x\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u6c42\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/p>\n<p>\u4e00\u65b9\u9762\uff0c\u6b63\u5f26\u7684\u5bfc\u6570\u662f\u4f59\u5f26\uff0c\u56e0\u6b64\u5916\u51fd\u6570\u7684\u5bfc\u6570\u5c06\u662f\u4f59\u5f26\uff0c\u5176\u53c2\u6570\u4e0e\u6b63\u5f26\u76f8\u540c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4b784343e9e483f8f3e2bb0cd465335_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}(x^3+7x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\text{cos}(x^3+7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"522\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0cx <sup>3<\/sup> +7x \u7684\u5bfc\u6570\u662f 3x <sup>2<\/sup> +7\u3002<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-395ee5862baf231657c05660e22bbd42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^3+7x\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=3x^2+7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"392\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\u662f\u4e24\u4e2a\u5bfc\u6570\u7684\u4e58\u79ef\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33416ac7184def2290a0a84cbd55a9b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black}z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5b44098b23fd39005532d5f42593f585_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3+7x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^3+7x)\\cdot (3x^2+7)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"555\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-con-la-regla-de-la-cadena\"><\/span>\u7528\u94fe\u5f0f\u6cd5\u5219\u89e3\u51b3\u5bfc\u6570\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bfc\u51fa\u4ee5\u4e0b\u590d\u5408\u51fd\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b84ea805fb8c56d493151d0f9b72b628_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(5x^2-6x\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"149\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5916\u51fd\u6570\u662f\u52bf\u51fd\u6570\uff0c\u56e0\u6b64\u8981\u8ba1\u7b97\u5176\u5bfc\u6570\uff0c\u5fc5\u987b\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82e232ad4bd7b0f1b4b93625bd8dcf2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=a\\bigl(g(x)\\bigr)^n \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=n\\cdot a\\bigl(g(x)\\bigr)^{n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"397\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-058311927ac43c45c1de7d799d802310_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\left(5x^2-6x\\right)^3\\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= 3\\left(5x^2-6x\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"415\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u8ba1\u7b97\u91cc\u9762\u51fd\u6570\u7684\u5bfc\u6570\u3002\u5b83\u662f\u5e42\u7684\u51cf\u6cd5\uff0c\u56e0\u6b64\u8981\u8ba1\u7b97\u5176\u5bfc\u6570\uff0c\u60a8\u5fc5\u987b\u5c06\u4ee5\u4e0b\u516c\u5f0f\u5e94\u7528\u4e8e\u5176\u6bcf\u4e00\u9879\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eda0577ba91756ce6852219b0b1bf4c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=ax^n \\ \\longrightarrow \\ f'(x)=n\\cdot ax^{n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b4b1fc6c2a94bb4e9833be8140196f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=5x^2-6x\\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1c9d99adf81a8861bbd2dee3b8a7fcee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g'(x)=2\\cdot 5x^1-1 \\cdot 6 x^0 =10x-6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7b80\u800c\u8a00\u4e4b\uff0c\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\u662f\u627e\u5230\u7684\u4e24\u4e2a\u5bfc\u6570\u7684\u4e58\u79ef\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3e6ffbcb906ced150b00cf463b56434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(5x^2-6x\\right)^3 \\ \\longrightarrow \\ \\bm{f'(x)= 3\\left(5x^2-6x\\right)^2\\cdot (10x-6)}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"450\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u89e3\u4ee5\u4e0b\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c6ecb2411e5245a58c614748280b4568_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-3\\left(5x^5+9x^3\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"182\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u6c42\u5916\u51fd\u6570\u7684\u5bfc\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e5d21c7196c7ebaeaf6ca11762ca251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr) &amp; =4 \\cdot ( -3) \\left(5x^5+9x^3\\right)^3 \\\\[1.5ex]&amp;=-12\\left(5x^5+9x^3\\right)^3 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"357\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u6c42\u89e3\u5185\u90e8\u51fd\u6570\u7684\u5bfc\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe839a2f2eb9412f63700dab70bf18f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=5x^5+9x^3\\ \\longrightarrow \\ g'(x)=25x^4+27x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"335\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0fe8c7e374a30ed8bcf0a83cea68d6bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-3\\left(5x^5+9x^3\\right)^4 \\ \\longrightarrow \\ \\bm{f'(x)=-12\\left(5x^5+9x^3\\right)^3\\cdot \\left(25x^4+27x^2\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"549\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u8ba1\u7b97\u4ee5\u4e0b\u51fd\u6570\u7ec4\u5408\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-555bcc9c8b61b47c73e2014749954305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{2x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"87\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5b83\u662f\u4e00\u4e2a\u6307\u6570\u51fd\u6570\uff0c\u56e0\u6b64\u8981\u8ba1\u7b97\u5176\u5bfc\u6570\uff0c\u5fc5\u987b\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f52dc9e8ea936ea4de492bb3be18ebb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{x} \\ \\longrightarrow \\ f'(x)=e^{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"204\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02e55bcf16e8288e1729ed5a4d06ed9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=e^{2x^3} \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= e^{2x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"281\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8fd8\u5c06\u51fd\u6570\u4e0e\u51fd\u6570\u7684\u6307\u6570\u533a\u5206\u5f00\u6765\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b17b1c7b9b871d8404166d92d5cb0974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=2x^3 \\ \\longrightarrow \\ g'(x)=6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u6574\u6570\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad4635f85ae781dd1565a8f6581d26c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{2x^3} \\ \\longrightarrow \\ \\bm{f'(x)= e^{2x^3}\\cdot 6x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u4ee5\u4e0b\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a10feee3fd85abefa9ec5ea79c0cf223_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{\\text{sen}(x) +x }\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8fd9\u662f\u51fd\u6570\u7684\u7ec4\u5408\uff0c\u56e0\u4e3a\u65e0\u7406\u51fd\u6570\u7684\u53c2\u6570\u4e2d\u6709\u4e00\u4e2a\u6b63\u5f26\u51fd\u6570\u548c\u4e00\u4e2a\u7ebf\u6027\u51fd\u6570\u3002\u6240\u4ee5\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u6839\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-64a603462f094d4c699c56453463ca49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x} \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"265\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e909efbe50930f94cce0b2485b060046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\sqrt[3]{\\text{sen}(x) +x } \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= \\cfrac{1}{3\\sqrt[3]{\\bigl(\\text{sen}(x) +x\\bigr)^2 }}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"455\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u4ece\u6fc0\u8fdb\u6d3e\u4e2d\u5f97\u51fa\u8fd9\u4e2a\u8bba\u70b9\u3002\u5b83\u662f\u51fd\u6570\u7684\u548c\uff0c\u56e0\u6b64\u5bfc\u6570\u5c06\u662f\u6bcf\u4e00\u9879\u7684\u5bfc\u6570\u4e4b\u548c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ffa1d177a8dfe81684225dffd555e6fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=\\text{sen}(x) +x \\ \\longrightarrow \\ g'(x)=\\cos(x) + 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"326\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\u7b49\u4e8e\u4e24\u4e2a\u8ba1\u7b97\u5bfc\u6570\u7684\u4e58\u79ef\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fad132b49a5faab86a3955efd5422973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f(x)=\\sqrt[3]{\\text{sen}(x)+x} \\ \\longrightarrow \\ f'(x)&amp; = \\cfrac{1}{3\\sqrt[3]{\\bigl(\\text{sen}(x) +x\\bigr)^2 }} \\cdot \\bigl(\\cos(x) + 1 \\bigr)\\\\[1.5ex]&amp;=\\cfrac{\\bm{\\cos(x) + 1}}{\\bm{3\\sqrt[3]{\\bigl(\\mathbf{sen}(x) +x\\bigr)^2} }}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"509\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bfc\u51fa\u4ee5\u4e0b\u51fd\u6570\u7ec4\u5408\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09f37b7970003fc0221e15dccc157ccf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x^2+5}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"100\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\uff0c\u60a8\u5fc5\u987b\u6c42\u5e42\u548c\u591a\u9879\u5f0f\u7684\u5bfc\u6570\uff0c\u7136\u540e\u5c06\u5b83\u4eec\u76f8\u4e58\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u5f97\u51fa\u529f\u7387\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9fb428e4d74e0f972130fde4e48ac0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=a^x \\ \\longrightarrow \\ f'(x)=a^x\\cdot \\ln (a)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"256\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1d18c3443d6398dcefba063ac556cbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=3^{x^2+5} \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= 3^{x^2+5}\\cdot  \\ln(3)\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"355\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u6b21\uff0c\u6211\u4eec\u4ece\u6307\u6570\u5bfc\u51fa\u591a\u9879\u5f0f\u51fd\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6070c83f8944ee39ae4e3e6e125bcc72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^2+5 \\ \\longrightarrow \\ g'(x)=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"235\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u800c\u94fe\u5f0f\u6cd5\u5219\u544a\u8bc9\u6211\u4eec\uff0c\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\u5c31\u662f\u6211\u4eec\u521a\u521a\u627e\u5230\u7684\u5bfc\u6570\u7684\u4e58\u79ef\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bc0c78749a089e832984e3844345b6f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3^{x^2+5} \\ \\longrightarrow \\ \\bm{f'(x)= 3^{x^2+5}\\cdot  \\ln(3) \\cdot 2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"337\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e606 <\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c85e9125bf4f54041c798dc4cc8975d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln \\bigl(4x^2 \\cdot \\cos(x) \\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"174\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u663e\u7136\uff0c\u8fd9\u4e2a\u95ee\u9898\u4e2d\u7684\u51fd\u6570\u662f\u590d\u5408\u51fd\u6570\uff0c\u56e0\u4e3a\u5728\u81ea\u7136\u5bf9\u6570\u7684\u53c2\u6570\u4e2d\uff0c\u6211\u4eec\u6709\u4e24\u79cd\u4e0d\u540c\u7c7b\u578b\u51fd\u6570\u7684\u4e58\u79ef\u3002\u6240\u4ee5\u6211\u4eec\u9996\u5148\u5bf9\u5bf9\u6570\u6c42\u5bfc\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a18d7f43ff1861389379485ae00db981_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x) \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"223\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b6ac8614a0671889738a762d0be9c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\ln \\bigl(4x^2 \\cdot \\cos(x) \\bigr) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)= \\cfrac{1}{4x^2 \\cdot \\cos(x) }\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"430\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u6b21\uff0c\u6211\u4eec\u4ece\u5bf9\u6570\u53c2\u6570\u5bfc\u51fa\u51fd\u6570\u3002\u8fd9\u662f\u4e24\u4e2a\u51fd\u6570\u7684\u4e58\u6cd5\uff0c\u56e0\u6b64\u5fc5\u987b\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8fdb\u884c\u63a8\u5bfc\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd35f94998c8450bd2e65e92eeecea2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x) \\cdot g(x) \\ \\longrightarrow \\ z'(x)=f'(x)\\cdot g(x)+f(x) \\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"439\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-643ddf7ec82cbcc3bc685ceadf59da98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}g(x)=4x^2 \\cdot \\cos(x) \\ \\longrightarrow \\ g'(x) &amp; = 8x\\cdot \\cos(x) + 4x^2 \\cdot \\bigl(- \\text{sen}(x)\\bigr) \\\\[2ex] &amp; = 8x\\cdot \\cos(x) - 4x^2 \\cdot  \\text{sen}(x)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"472\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6839\u636e\u94fe\u5f0f\u6cd5\u5219\uff0c\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\u5c06\u662f\u4e24\u4e2a\u5bfc\u6570\u7684\u4e58\u79ef\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6912d0951fb85a61df21cbed282000f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;= \\cfrac{1}{4x^2 \\cdot \\cos(x) } \\cdot \\bigl( 8x\\cdot \\cos(x) - 4x^2 \\cdot  \\text{sen}(x) \\bigr)\\\\[1.5ex]&amp;=\\cfrac{8x\\cdot \\cos(x) - 4x^2 \\cdot\\text{sen}(x)}{4x^2 \\cdot \\cos(x)}\\\\[1.5ex]&amp;=\\cfrac{\\bm{2\\cos(x) - x \\cdot }\\mathbf{sen}\\bm{(x)}}{\\bm{x \\cdot \\cos(x) }}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"169\" width=\"368\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e607<\/h3>\n<p>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u89e3\u4ee5\u4e0b\u51fd\u6570\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3eb7a0c588b3aac39a2a4aa49a691598_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_9 (e^{x^2}-6x^7)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8fd9\u662f\u4e00\u4e2a\u51fd\u6570\u7684\u7ec4\u5408\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u5bf9\u6570\u53ca\u5176\u53c2\u6570\u5206\u522b\u5fae\u5206\uff0c\u7136\u540e\u4e58\u4ee5\u5bfc\u6570\u3002<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u9996\u5148\u6211\u4eec\u5bf9\u4ee5 9 \u4e3a\u5e95\u7684\u5bf9\u6570\u6c42\u5fae\u5206\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c3339cb70e45253b4994a0c740202cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a (x) \\ \\longrightarrow \\ f'(x)=\\cfrac{1}{x\\cdot \\ln (a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"289\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0b4fc286244d6e5e35b8f7e94961314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\log_9 (e^{x^2}-6x^7) \\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=\\cfrac{1}{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"479\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u5bf9\u6570\u53c2\u6570\u7684\u5bfc\u6570\u3002\u8bf7\u6ce8\u610f\uff0c\u6570\u5b57 e \u7684\u53c2\u6570\u4e2d\u6709\u4e00\u4e2a\u51fd\u6570\uff0c\u5373\u5b83\u662f\u4e00\u4e2a\u590d\u5408\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u8fd8\u9700\u8981\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u63a8\u5bfc\u8be5\u51fd\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34065617ade6fb28fe66bc3f57a49cd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"h(x)=e^{x^2} \\ \\longrightarrow \\ h'(x)=e^{x^2}\\cdot \\bigl(x^2\\bigr)' =e^{x^2}\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"348\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5bf9\u6570\u6574\u6570\u53c2\u6570\u7684\u5bfc\u6570\u5c06\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f7cd729a06f3cde16890b587693a667_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)= e^{x^2}-6x^7\\ \\longrightarrow \\ g'(x)=e^{x^2}\\cdot 2x - 42x^6\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"352\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\u5c06\u662f f'(g(x)) \u548c g'(x) \u7684\u4e58\u79ef\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a702df902c9f1eff66e14836a262c0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{1}{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)} \\cdot \\bigl(e^{x^2}\\cdot 2x - 42x^6\\bigr)\\\\[1.5ex]&amp;=\\cfrac{\\bm{e^{x^2}\\cdot 2x - 42x^6}}{\\bm{\\bigl(e^{x^2}-6x^7\\bigr)\\cdot \\ln(9)}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"342\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e608<\/h3>\n<p>\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bfc\u51fa\u4ee5\u4e0b\u590d\u5408\u51fd\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0fa2f9b67e41d5edc5bbef249f598359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"231\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u672c\u7ec3\u4e60\u4e2d\uff0c\u6211\u4eec\u6709\u591a\u4e2a\u51fd\u6570\u7684\u7ec4\u5408\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u591a\u6b21\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u3002\u6211\u4eec\u9996\u5148\u4ece\u6b63\u5f26\u5bfc\u51fa\u4e09\u89d2\u51fd\u6570\uff0c\u5176\u5bfc\u6570\u662f\u4f59\u5f26\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b6d04ed6e1b20f210641bb48c25c2c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\\ \\longrightarrow \\ f'\\bigl(g(x)\\bigr)=\\cos\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"569\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u8ba1\u7b97\u6b63\u5f26\u53c2\u6570\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e1c2492990456e277e493c898cb3924_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} g(x)= \\Bigl( 9x^5 + \\cos(x) \\Bigr)^2 \\cdot g'(x) &amp;= 2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(9x^5 + \\cos(x) \\Bigr)' \\\\[1.5ex]&amp;=2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(45x^4-\\text{sen}(x)\\Bigr)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"519\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u518d\u6b21\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u5f97\u5230\u6574\u4e2a\u51fd\u6570\u7ec4\u5408\u7684\u5bfc\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8abee37ef3d49cc56596417a2e31618f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f\\bigl(g(x)\\bigr) \\ \\longrightarrow \\ z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db5ac3368ea7d37f280e0f538aaed1a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{f'(x)=\\cos } \\bm{\\biggl( \\Bigl(9x^5 + \\cos(x) \\Bigr)^2 \\biggr) \\cdot 2\\Bigl(9x^5 + \\cos(x) \\Bigr) \\cdot \\Bigl(45x^4-}\\mathbf{sen}\\bm{(x)\\Bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"510\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-regla-de-la-cadena\"><\/span>\u94fe\u5f0f\u6cd5\u5219\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u8bc1\u660e\u94fe\u5f0f\u6cd5\u5219\u516c\u5f0f\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4ece\u5bfc\u6570\u7684\u6570\u5b66\u5b9a\u4e49\u5f00\u59cb\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc1699622d128f888c1f20599aeccf60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"219\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u4ee4<em>z<\/em>\u4e3a\u7531\u4e24\u4e2a\u51fd\u6570\u7ec4\u6210\u7684\u51fd\u6570\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a650ba7c58d41f371d90a56e4d4fd4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z=f\\bigl(g(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"90\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u90a3\u4e48\u5e94\u7528\u8be5\u5b9a\u4e49\u7684\u51fd\u6570<em>z<\/em>\u7684\u5bfc\u6570\u5c06\u662f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9419bc1d5617600c2ffea842822efed7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"269\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u5982\u60a8\u6240\u77e5\uff0c\u60a8\u53ef\u4ee5\u5c06\u5206\u6570\u4e58\u4ee5\u6216\u9664\u4ee5\u540c\u4e00\u9879\uff0c\u56e0\u4e3a\u8fd9\u4e0d\u4f1a\u6539\u53d8\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u7ee7\u7eed\u4e0b\u4e00\u6b65\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-18ff4ca3bcd8ba04a25aa0187b3b5b3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{h}\\cdot \\frac{g(x+h)-g(x)}{g(x+h)-g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u91cd\u65b0\u6392\u5217\u5206\u6570\u7684\u5206\u6bcd\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9059bbff916941c2e161b6d127ec654e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{g(x+h)-g(x)}\\cdot \\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u901a\u8fc7\u5e94\u7528\u6781\u9650\u7684\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u4e0a\u8ff0\u6781\u9650\u4e00\u5206\u4e3a\u4e8c\u3002\u7531\u4e8e\u4e58\u79ef\u7684\u6781\u9650\u7b49\u4e8e\u6781\u9650\u7684\u4e58\u79ef\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-220a40fee3825089394f3d6e5578c4eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f\\bigl(g(x+h)\\bigr)-f\\bigl(g(x)\\bigr)}{g(x+h)-g(x)}\\cdot \\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"436\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u7b49\u4ef7\u4e8e\u4ee5\u4e0b\u5185\u5bb9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8188c6fac1c61928975e7a8c02ac79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f'\\bigl(g(x)\\bigr)\\cdot g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"175\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u94fe\u5f0f\u6cd5\u5219\u516c\u5f0f\u88ab\u8bc1\u660e\u4e86\uff0c\u56e0\u4e3a\u6211\u4eec\u662f\u4ece\u5bfc\u6570\u7684\u5b9a\u4e49\u5f97\u51fa\u5b83\u7684\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u94fe\u5f0f\u6cd5\u5219\u4ee5\u53ca\u5982\u4f55\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u5bfc\u51fa\u51fd\u6570\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6c42\u89e3\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%b4%be%e7%94%9f%e8%a7%84%e5%88%99%e9%93%be\/\"> <span class=\"screen-reader-text\">\u94fe\u5f0f\u6cd5\u5219\uff08\u5bfc\u6570\uff09<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[6],"tags":[],"class_list":["post-37","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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