{"id":370,"date":"2023-07-03T19:47:19","date_gmt":"2023-07-03T19:47:19","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%a0%b9%e5%bc%8f%e6%97%a0%e7%90%86%e6%a0%b9%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-07-03T19:47:19","modified_gmt":"2023-07-03T19:47:19","slug":"%e6%a0%b9%e5%bc%8f%e6%97%a0%e7%90%86%e6%a0%b9%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%a0%b9%e5%bc%8f%e6%97%a0%e7%90%86%e6%a0%b9%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u6e90\u4e8e\u6839"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u6c42\u6839\uff08\u6216\u6839\u5f0f\u51fd\u6570\uff09\u7684\u5bfc\u6570\u3002\u60a8\u5c06\u627e\u5230\u6839\u9664\u6cd5\u7684\u516c\u5f0f\u4ee5\u53ca\u6839\u7684\u5bfc\u6570\u7684\u9010\u6b65\u6c42\u89e3\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-raiz\"><\/span>\u6839\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6839\u6216\u65e0\u7406\u51fd\u6570\u7684\u5bfc\u6570<\/strong>\u7b49\u4e8e\u88ab\u88ab\u6570\uff08\u6839\u5f0f\u4e0b\u9762\u7684\u8868\u8fbe\u5f0f\uff09\u7684\u5bfc\u6570\u9664\u4ee5\u6839\u7684\u6307\u6570\u4e58\u4ee5\u540c\u6839\u7684\u4e58\u79ef\uff0c\u518d\u4ece\u88ab\u88ab\u6570\u7684\u6307\u6570\u4e2d\u51cf\u53bb 1\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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u4f46\u662f\uff0c\u5982\u679c\u6839\u88ab\u6570\u53ea\u662f x\uff0c\u5219\u516c\u5f0f\u4f1a\u7b80\u5316\u3002\u56e0\u6b64 x \u7684\u6839\u5bfc\u6570\u5982\u4e0b\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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u6c42\u6839\u7684\u516c\u5f0f\u6709\u4e24\u4e2a\uff1a\u7b2c\u4e00\u4e2a\u603b\u662f\u53ef\u4ee5\u4f7f\u7528\uff0c\u7b2c\u4e8c\u4e2a\u53ea\u6709\u5f53\u88ab\u6570\u4e3a x \u65f6\u624d\u53ef\u4ee5\u4f7f\u7528\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\/derive-dune-racine.webp\" alt=\"\u6e90\u4e8e\u4e00\u4e2a\u6839\" class=\"wp-image-1787\" width=\"361\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5982\u679c\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u5206\u6570\u5206\u5b50\u4e2d\u7684\u9879\u662f\u5728\u6c42\u6839\u7684\u5bfc\u6570\u65f6\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u5f97\u5230\u7684\u7ed3\u679c\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5f53\u88ab\u6570\u4e3a x \u65f6\uff0c1 \u51fa\u73b0\u5728\u5206\u6bcd\u4e2d\uff0c\u56e0\u4e3a\u5b83\u662f x \u7684\u5bfc\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-raices\"><\/span>\u6839\u5bfc\u6570\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u6839\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\uff0c\u4e0b\u9762\u6211\u4eec\u5c06\u89e3\u91ca\u6b64\u7c7b\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5982\u4f55\u6c42\u6839\u7684\u5bfc\u6570\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-raiz-cuadrada\"><\/span>\u793a\u4f8b 1\uff1a\u5e73\u65b9\u6839\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7136\u540e\u6211\u4eec\u5c06\u770b\u5230\u5e73\u65b9\u6839\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\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-12533a178fbfb7d1a6b3175d2a812cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6839\u5185\u90e8\u7684\u8868\u8fbe\u5f0f\u53ea\u662f\u4e00\u4e2a x\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u4f7f\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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5e73\u65b9\u6839\u7684\u5bfc\u6570\u7b49\u4e8e 1 \u9664\u4ee5 2 \u4e58\u4ee5 x \u7684\u5e73\u65b9\u6839\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-5e879d493e8b67755617d2aed1743cde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{2\\sqrt{x^{2-1}}}=\\cfrac{1}{2\\sqrt{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"425\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-raiz-cubica\"><\/span>\u793a\u4f8b 2\uff1a\u7acb\u65b9\u6839\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/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-c3c5e7be9bc257eb2866277bae5be644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6839\u4e0b\u7684\u8868\u8fbe\u5f0f\u662fx\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\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-6f42caa889f09dbf2af835915f0f6b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7acb\u65b9\u6839\u7684\u5bfc\u6570\u7b49\u4e8e 1 \u9664\u4ee5 3 \u4e58\u4ee5 x \u5e73\u65b9\u6839\u7684\u7acb\u65b9\u6839\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-f0e928affa231f99c8af7ebffb25049b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{3\\sqrt[3]{x^{3-1}}}=\\cfrac{1}{3\\sqrt[3]{x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"436\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-raiz-cuarta\"><\/span>\u793a\u4f8b 3\uff1a\u56db\u6b21\u65b9\u6839\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/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-4a02a76ecccf5f654e0a9f7c3fb570e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[4]{7x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u7684\u6839\u53f7\u4e0b\u9762\u6ca1\u6709x\uff0c\u4f46\u662f\u6211\u4eec\u786e\u5b9e\u6709\u4e00\u4e2a\u66f4\u590d\u6742\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u6839\u5bfc\u6570\u7684\u4e00\u822c\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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u6839\u5f0f\u4e0b\u7684\u8868\u8fbe\u5f0f\u662f\u4e00\u6b21\u51fd\u6570\uff0c\u56e0\u6b64\u5b83\u7684\u5bfc\u6570\u4e3a7\u3002\u56e0\u6b64\uff0c\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-d406850e42a532ebe3209ac6d705b0db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[4]{7x-2}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{7}{4\\sqrt[4]{(7x-2)^3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"446\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-4-derivada-de-una-raiz-dentro-de-otra\"><\/span>\u793a\u4f8b 4\uff1a\u4ece\u4e00\u4e2a\u6839\u5230\u53e6\u4e00\u4e2a\u6839\u7684\u63a8\u5bfc<span class=\"ez-toc-section-end\"><\/span><\/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-5955c2ba5e8301beb45ec4fe7207b601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt{x^2+\\sqrt[3]{x^4-5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"180\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u6c42\u89e3\u8fd9\u4e2a\u6839\u7531\u53e6\u4e00\u4e2a\u6839\u7ec4\u6210\u7684\u5bfc\u6570\uff0c\u6211\u4eec\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-d68fa956b939a4e9a483fc43509a3e5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[n]{u}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{u'}{n\\sqrt[n]{u^{n-1}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"374\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u60a8\u5fc5\u987b\u8fde\u7eed\u4e24\u6b21\u4f7f\u7528\u76f8\u540c\u7684\u516c\u5f0f\u6765\u8ba1\u7b97\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-c37131b50bda38022296c6401af727ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp; =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot\\left(x^2+\\sqrt[3]{x^4-5}\\right)' \\\\[3ex]&amp;\\displaystyle =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot \\left(2x+\\frac{1}{ 3\\sqrt[3]{(x^4-5)^2}}\\cdot (x^4-5)'\\right)\\\\[3ex]&amp;\\displaystyle =\\cfrac{1}{2\\sqrt{x^2+\\sqrt[3]{x^4-5}}}\\cdot \\left(2x+\\frac{1}{ 3\\sqrt[3]{(x^4-5)^2}}\\cdot 4x^3\\right)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"211\" width=\"453\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-una-raiz\"><\/span>\u89e3\u51b3\u4e86\u6839\u7684\u5bfc\u6570\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\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-3f3ee60a40f0696dc0b5ef1e5bda06ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\sqrt[5]{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" 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-e9589007466797e244646623ece04655_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\sqrt[3]{x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"117\" 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-983ef87ac1eca3d1e963de48bb867531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\sqrt{x^2-4x+9}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"189\" 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-24340e19537976608651d3554d8f47b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\sqrt[4]{x^9+5x^4-2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"207\" 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-4f82a43408b63e2399ec88e8a3e2e868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\sqrt[5]{3(x^2-1)^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"181\" style=\"vertical-align: -6px;\"><\/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-5280308e036830e09c0bdcd8bd8791fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\sqrt[6]{x^2+4(5x^3-8x)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"239\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-572ec9e7f3b912e18b40787ac9b212b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{1}{5\\sqrt[5]{x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"134\" 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-3bacf51d3e3fd8fa192f982456f2a8d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{4x^3}{3\\sqrt[3]{\\left(x^4\\right)^2}}= \\cfrac{4x^3}{3\\sqrt[3]{x^8}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"225\" style=\"vertical-align: -30px;\"><\/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-3dbbfa5053cc4b46f21eee7a842a00c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=\\cfrac{2x-4}{2\\sqrt{x^2-4x+9}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"204\" 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-5169c93bdfa2522a3219563eee1bb354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=\\cfrac{9x^8+20x^3-2}{4\\sqrt[4]{\\left(x^9+5x^4-2x\\right)^3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"248\" style=\"vertical-align: -30px;\"><\/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-f68dce6e62d98d10d99daf57e0128069_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{3\\cdot 4 \\cdot (x^2-1)^3\\cdot 2x}{5\\sqrt[5]{\\left(3\\left(x^2-1\\right)^4\\right)^4}}=\\cfrac{24x(x^2-1)^3}{5\\sqrt[5]{81\\left(x^2-1\\right)^{16}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"386\" style=\"vertical-align: -41px;\"><\/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-dd1d3bbced66caaed0ac254363e5f2f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{2x+2\\cdot 4(5x^3-8x)\\cdot (15x^2-8)}{6\\sqrt[6]{\\left(x^2+4(5x^3-8x)^2\\right)^5}}=\\cfrac{2x+8(5x^3-8x)(15x^2-8)}{6\\sqrt[6]{\\left(x^2+4(5x^3-8x)^2\\right)^5}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"571\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u6c42\u6839\uff08\u6216\u6839\u5f0f\u51fd\u6570\uff09\u7684\u5bfc\u6570\u3002\u60a8\u5c06\u627e\u5230\u6839\u9664\u6cd5\u7684\u516c\u5f0f\u4ee5\u53ca\u6839\u7684\u5bfc\u6570\u7684\u9010\u6b65\u6c42\u89e3\u7ec3\u4e60\u3002 \u6839\u7684\u5bfc\u6570\u516c\u5f0f  &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%a0%b9%e5%bc%8f%e6%97%a0%e7%90%86%e6%a0%b9%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u6e90\u4e8e\u6839<\/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-370","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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