{"id":28,"date":"2023-09-17T11:03:43","date_gmt":"2023-09-17T11:03:43","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8a%9f%e7%8e%87%e5%8a%bf%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-09-17T11:03:43","modified_gmt":"2023-09-17T11:03:43","slug":"%e5%8a%9f%e7%8e%87%e5%8a%bf%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%8a%9f%e7%8e%87%e5%8a%bf%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u5e42\uff08\u6216\u52bf\u51fd\u6570\uff09\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u5e42\uff08\u6216\u52bf\u51fd\u6570\uff09\uff0c\u60a8\u5c06\u627e\u5230\u5e42\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u51e0\u4e2a\u793a\u4f8b\uff0c\u60a8\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-potencia\"><\/span>\u5e42\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5e42\u6216\u52bf\u51fd\u6570\u7684\u5bfc\u6570\u662f\u5e42\u7684\u6307\u6570\u4e58\u4ee5\u5e95\u6570\u7684\u6307\u6570\u51cf\u53bb 1 \u4e58\u4ee5\u5e95\u6570\u7684\u5bfc\u6570\u7684\u4e58\u79ef\u3002<\/strong><\/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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u57fa\u6570\u662f<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6052\u7b49\u51fd\u6570\/\">\u6052\u7b49\u51fd\u6570<\/a><\/span>\uff0c\u8981\u5f97\u5230\u5e42\uff0c\u53ea\u9700\u5c06\u51fd\u6570\u4e58\u4ee5\u6307\u6570\uff0c\u7136\u540e\u4ece\u6307\u6570\u4e2d\u51cf\u53bb\u4e00\u4e2a\u5355\u4f4d\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-46eb5b8a4c6968ca5e37af417fd2fb31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u6052\u7b49\u51fd\u6570\u7684\u5bfc\u6570\u7b49\u4e8e 1\u3002<\/p>\n<p>\u603b\u4e4b\uff0c\u8981\u5bfc\u51fa\u52bf\u51fd\u6570\uff0c\u6709\u4e24\u4e2a\u516c\u5f0f\uff1a\u7b2c\u4e00\u4e2a\u516c\u5f0f\u59cb\u7ec8\u53ef\u7528\uff0c\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4ec5\u5f53\u5e95\u4e3a x \u65f6\u624d\u9002\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\/derivee-dune-puissance.webp\" alt=\"\u6e90\u4e8e\u4e00\u79cd\u529b\u91cf\" class=\"wp-image-1760\" width=\"354\" height=\"264\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u6211\u4eec\u53ef\u4ee5\u8f7b\u677e\u9a8c\u8bc1\u5e42\u5bfc\u6570\u7684\u7b2c\u4e00\u4e2a\u516c\u5f0f\u4e0e\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u76f8\u4f3c\uff0c\u4f46\u5e94\u7528\u4e86\u94fe\u5f0f\u6cd5\u5219\u3002<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u8fd9\u4e9b\u516c\u5f0f\u4ec5\u5f53\u53d8\u91cf\u662f\u5e42\u7684\u5e95\u6570\u65f6\u624d\u80fd\u4f7f\u7528\uff0c\u5982\u679c x \u4f4d\u4e8e\u5206\u6bcd\u4e2d\uff0c\u5219\u5fc5\u987b\u5e94\u7528\u6307\u6570\u51fd\u6570\u5bfc\u6570\u7684\u89c4\u5219\uff1a<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6307\u6570\u51fd\u6570\u7684\u5bfc\u6570\/\">\u6307\u6570\u51fd\u6570\u7684\u5bfc\u6570<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-potencias\"><\/span>\u5e42\u5bfc\u6570\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u52bf\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u6b64\u7c7b\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5e42\u662f\u5982\u4f55\u5bfc\u51fa\u7684\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-potencia-de-base-x\"><\/span>\u793a\u4f8b 1\uff1a\u57fa\u6570 x \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-1a77d84e8f9a9d165a989ae8edd67a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u4e00\u8282\u4e2d\u6240\u89e3\u91ca\u7684\uff0c\u5f53\u5e42\u7684\u5e95\u6570\u4ec5\u4e3a x \u65f6\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\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-46eb5b8a4c6968ca5e37af417fd2fb31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"355\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0cx \u6b21\u65b9 4 \u6b21\u65b9\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-b4f99a41ebf24ffb9dc9d375925fbb03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=4\\cdot x^{4-1}=4x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-potencia-con-parentesis\"><\/span>\u793a\u4f8b 2\uff1a\u5e26\u62ec\u53f7\u7684\u5e42\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-c7e7bcf1cc01f1609b200eb0707450f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(2x-1)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u57fa\u6570\u4e0d\u662f\u6052\u7b49\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u5e42\u5bfc\u6570\u7684\u901a\u7528\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u62ec\u53f7\u4e2d\u7684\u51fd\u6570\u662f\u7ebf\u6027\u51fd\u6570\uff0c\u56e0\u6b64\u5b83\u7684\u5bfc\u6570\u4e3a2\u3002\u56e0\u6b64\uff0c\u6574\u4e2a\u52bf\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-8b3fb5d76dac22c3fad5ebe3a0cae630_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(2x-1)^5 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=5\\cdot (2x-1)^4\\cdot 2=10(2x-1)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"577\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-potencia-negativa\"><\/span>\u793a\u4f8b 3\uff1a\u8d1f\u5e42\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-0bb49a61d47e399ec84ffddce840b4a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(\\log 9x)^{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u6307\u6570\u4e3a\u8d1f\u4e14\u5e95\u6570\u4e3a\u5bf9\u6570\u7684\u52bf\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u5bf9\u8be5\u51fd\u6570\u8fdb\u884c\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5373\u4f7f\u5e42\u6307\u6570\u4e3a\u8d1f\u6570\uff0c\u4e5f\u5fc5\u987b\u51cf\u4e00\u3002\u56e0\u6b64\u8be5\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-b883e28fe86b43bae53225fbfc0989c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-2\\cdot (\\log 9x)^{-3}\\cdot \\cfrac{1}{9x\\cdot \\ln 10}\\cdot 9 =\\cfrac{-2(\\log 9x)^{-3}}{x\\ln 10}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"412\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u60a8\u5bf9\u89e3\u6cd5\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u53ef\u4ee5\u5728\u8fd9\u91cc\u67e5\u9605\u5bf9\u6570\u51fd\u6570\u5bfc\u6570\u7684\u516c\u5f0f\uff1a<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570-neperian-\u81ea\u7136\u5bf9\u6570\/\">\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-4-derivada-de-una-potencia-con-raiz\"><\/span>\u793a\u4f8b 4\uff1a\u5e26\u6839\u7684\u5e42\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-74c457eaa374d11591afb05c08c79a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\sqrt[3]{(5x+2)^7}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"149\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u6b64\u793a\u4f8b\u4e2d\u7684\u51fd\u6570\u662f\u6b63\u5219\u8868\u8fbe\u5f0f\u4e2d\u7684\u5e42\u3002\u7136\u800c\uff0c\u6839\u5f0f\u53ef\u4ee5\u8f6c\u6362\u4e3a\u52bf\u8868\u8fbe\u5f0f\uff0c\u56e0\u6b64\u53ef\u4ee5\u901a\u8fc7\u5c06\u5176\u8f6c\u6362\u4e3a\u5e26\u6709\u5206\u6570\u6307\u6570\u7684\u52bf\u51fd\u6570\u6765\u7b80\u5316\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-a851a10c275664fd40272c3f18ebb696_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=(5x+2)^{\\frac{7}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5e94\u7528\u53d8\u91cf\u5e42\u7684\u5bfc\u6570\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-54482f54c568a1e8f0e5706dd9ea1f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=u^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot u^{k-1}\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\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-48032a3f39b346214870d2930c0e070f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{7}{3}\\cdot (5x+2)^{\\frac{7}{3}-1} \\cdot 5=\\cfrac{35}{3}(5x+2)^{\\frac{4}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"314\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u60a8\u8fd8\u53ef\u4ee5\u4f7f\u7528\u6839\u5bfc\u6570\u89c4\u5219\u533a\u5206\u8fd9\u4e9b\u7c7b\u578b\u7684\u51fd\u6570\uff1a<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u89c1\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6839\u5f0f\u65e0\u7406\u6839\u51fd\u6570\u7684\u5bfc\u6570\/\">\u6e90\u81ea\u6839<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-una-potencia\"><\/span>\u89e3\u7b54\u4e86\u5e42\u5bfc\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u5e42\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-8439a4f480db3b28403219b3d6c617c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"101\" 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-586b1cce6da03d26fc251a34f15b8713_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=3x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"110\" 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-2048513ae93bb32ac7333db56114f8f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=-2x^{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" 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-61b9db052aa145257ef92ac543621b69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=(3x^2-4x)^6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" 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-234c4c2a85b56e062d186e33461534c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=6(x^2+10)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"170\" 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-888598e68e596f15e1e4b585c2287c4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\cfrac{1}{(9x+2)^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"156\" 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-bc2353357a484e175ac77e99e4446cb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G) } f(x)=\\sqrt{4x^5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" 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-3e21d4a7733a95b407d4a53114146489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H) } \\displaystyle f(x)=\\left(x^2-4x+\\frac{1}{3}\\right)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"210\" 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-c04e44f3e248cec297f4476885e22a25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I) } f(x)=\\text{sen}^3(6-2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"172\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32e3eaeb51430921053c75da627cacd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=8x^7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"115\" 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-44e8de4cfb9cb267005e390e06c393e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=15x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" 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-4394259c55b711c8668f4d72e3bd4766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=8x^{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"125\" 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-8a916b5238f094595e63d04a86303a7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=6(3x^2-4x)^5\\cdot (3x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"262\" 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-698c94329d2e6edc002bf2b99d4de74e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=3\\cdot 6(x^2+10)^2 \\cdot 2x=36x(x^2+10)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"358\" 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-b2c94d0e23facd72c3a85241bfc4552a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=-3\\cdot (9x+2)^{-4}\\cdot 9 =-27(9x+2)^{-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"363\" 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-9f488aced09f0e560280f5ce55a1b002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{G) } f'(x)=\\cfrac{5}{2}\\cdot 2x^{\\frac{5}{2}-1} =5x^{\\frac{3}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"211\" 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-19d1d31c8415cb654940148ec1a25835_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{H) } \\displaystyle f'(x)=4\\left(x^2-4x+\\cfrac{1}{3}\\right)^3\\cdot (2x-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"303\" style=\"vertical-align: -23px;\"><\/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-aa9c91854971313e88fde0d535c5a6c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{I) } f'(x)=3\\text{sen}^2(6-2x)\\cdot \\text{cos}(6-2x)\\cdot (-2)=-6x\\cdot \\text{sen}^2(6-2x)\\cdot \\text{cos}(6-2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"599\" style=\"vertical-align: -5px;\"><\/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\u5bfc\u51fa\u5e42\uff08\u6216\u52bf\u51fd\u6570\uff09\uff0c\u60a8\u5c06\u627e\u5230\u5e42\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u51e0\u4e2a\u793a\u4f8b\uff0c\u60a8\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%8a%9f%e7%8e%87%e5%8a%bf%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u5e42\uff08\u6216\u52bf\u51fd\u6570\uff09\u7684\u5bfc\u6570<\/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-28","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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