{"id":36,"date":"2023-09-17T11:00:46","date_gmt":"2023-09-17T11:00:46","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e9%99%a4%e5%95%86%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-09-17T11:00:46","modified_gmt":"2023-09-17T11:00:46","slug":"%e9%99%a4%e5%95%86%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e9%99%a4%e5%95%86%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u5546\uff08\u6216\u9664\u6cd5\uff09\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u4ece\u4e24\u4e2a\u51fd\u6570\u5bfc\u51fa\u5546\uff08\u6216\u9664\u6cd5\uff09\u3002\u60a8\u5c06\u627e\u5230\u51fd\u6570\u5546\u7684\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u5206\u6b65\u7ec3\u4e60\u6765\u7ec3\u4e60\u9664\u6cd5\u7684\u5bfc\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-un-cociente\"><\/span>\u5546\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u7684\u7cfb\u6570\uff08\u6216\u9664\u6cd5\uff09\u7684\u5bfc\u6570<\/strong>\u7b49\u4e8e\u5206\u5b50\u51fd\u6570\u9664\u4ee5\u5206\u6bcd\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u8be5\u5bfc\u6570\u5c0f\u4e8e\u5206\u5b50\u51fd\u6570\u9664\u4ee5\u5206\u6bcd\u51fd\u6570\u7684\u5bfc\u6570\u9664\u4ee5\u9ad8\u5206\u6bcd\u51fd\u6570\u5e73\u65b9\u7684\u503c\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-quotient-de-division-derivee.webp\" alt=\"\u9664\u6cd5\u6216\u5546\u7684\u5bfc\u6570\u516c\u5f0f\" class=\"wp-image-2194\" width=\"326\" height=\"304\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u5f53\u6211\u4eec\u5e94\u7528\u5546\uff08\u6216\u9664\u6cd5\uff09\u7684\u5bfc\u6570\u89c4\u5219\u65f6\uff0c\u5fae\u5206\u540e\u6211\u4eec\u4ecd\u7136\u6709\u4e00\u4e2a\u5206\u6570\u3002\u4f46\u662f\uff0c\u9664\u6b64\u4e4b\u5916\uff0c\u5206\u5b50\u4e2d\u6709\u4e24\u6b21\u4e58\u6cd5\u548c\u4e00\u6b21\u51cf\u6cd5\uff0c\u5206\u6bcd\u5219\u4e3a 2 \u6b21\u65b9\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-cocientes\"><\/span>\u5546\u7684\u5bfc\u6570\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u521a\u521a\u4e86\u89e3\u4e86\u4e24\u4e2a\u51fd\u6570\u7684\u5546\u7684\u5bfc\u6570\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u7136\u540e\u6211\u4eec\u5c06\u89e3\u51b3\u6b64\u7c7b\u8fd0\u7b97\u7684\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\u3002\u8bf7\u8bb0\u4f4f\uff0c\u5982\u679c\u60a8\u4e0d\u660e\u767d\u6cdb\u51fd\u5546\u662f\u5982\u4f55\u5f97\u51fa\u7684\uff0c\u53ef\u4ee5\u5728\u8bc4\u8bba\u90e8\u5206\u8be2\u95ee\u6211\u4eec\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b1<\/h3>\n<p>\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u63a8\u5bfc\u51fa\u4e00\u4e2a\u52bf\u51fd\u6570\u9664\u4ee5\u4e09\u89d2\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-9d260d4cdca9f28e43607a9c1e7b3404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{3x^2+4x}{\\text{sen}(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"128\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4e24\u4e2a\u4e0d\u540c\u51fd\u6570\u76f8\u9664\u7684\u5bfc\u6570\u516c\u5f0f\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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u6211\u4eec\u9996\u5148\u9700\u8981\u5206\u522b\u8ba1\u7b97\u6bcf\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\uff1a <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-21\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-24719cd47158514d54e16f4994a1c2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (3x^2+4x)=6x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"180\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-093fb274a2a393453833ed572dc1bc62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\text{sen}(2x)=2\\text{cos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"171\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\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-65ce4673f3ad5a4c09a9b2e7c611821d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{3x^2+4x}{\\text{sen}(2x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{(6x+4)\\cdot\\text{sen}(2x)-(3x^2+4x)\\cdot 2\\text{cos}(2x)}{\\text{sen}^2(2x)}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"380\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b2<\/h3>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u6c42\u4e00\u4e2a\u5e38\u6570\u9664\u4ee5\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-e7d5ddfdf95f11b94783ca40437e371a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{10}{x^2+3x-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"150\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u9762\u770b\u5230\u7684\uff0c\u4e24\u4e2a\u4e0d\u540c\u51fd\u6570\u9664\u6cd5\u7684\u5bfc\u6570\u89c4\u5219\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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5206\u522b\u8ba1\u7b97\u5206\u5b50\u548c\u5206\u6bcd\u7684\u5bfc\u6570\uff1a <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-24\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-191c03d69e261059308133b99f87bf1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 10=0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c63da81dbf763b0a24cf929aef024c51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^2+3x-9)=2x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"201\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u6c42\u51fa\u6574\u6570\u9664\u6cd5\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-8f8bdea77dc91b1aff40695511593e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{10}{x^2+3x-9}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{0\\cdot (x^2+3x-9)-10\\cdot (2x+3)}{\\left(x^2+3x-9\\right)^2}=\\cfrac{-20x+30}{\\left(x^2+3x-9\\right)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"441\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u5f53\u5206\u5b50\u4e2d\u6709\u4e00\u4e2a\u5e38\u6570\u9664\u4ee5\u4e00\u4e2a\u51fd\u6570\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5bfc\u51fa\u4e00\u4e2a\u516c\u5f0f\u6765\u6c42\u5bfc\uff0c\u56e0\u4e3a\u8be5\u5e38\u6570\u7684\u5bfc\u6570\u59cb\u7ec8\u4e3a0\u3002\u56e0\u6b64\uff0c\u4ee5\u4e0b\u516c\u5f0f\u5c06\u59cb\u7ec8\u4e3a\u771f\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-1f0bd615634f5205f91674f96f5c2514_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}z(x)=\\cfrac{k}{f(x)} \\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{-k\\cdot f'(x)}{\\bigl(f(x)\\bigr)^2}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b3<\/h3>\n<p>\u5728\u672c\u7ec3\u4e60\u4e2d\uff0c\u6211\u4eec\u5c06\u5bfc\u51fa\u4e24\u4e2a\u591a\u9879\u5f0f\u7684\u5546\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-59b390fee61ab3c2cbb4dc2230386658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u6c42\u89e3\u5bfc\u6570\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u4e24\u4e2a\u4e0d\u540c\u51fd\u6570\u7684\u5546\u7684\u5bfc\u6570\u89c4\u5219\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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u6c42\u5206\u5b50\u591a\u9879\u5f0f\u548c\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u5bfc\u6570\uff1a <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-27\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-39e82139a124bf031f31b84007bcb923_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^3+4x^2)=3x^2+8x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"196\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-73db77f7639fc8b4cc305fbbb2b1cf2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (5x^2-8)=10x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"148\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u591a\u8bcd\u9664\u6cd5\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-065ad49556f264b4cfb505522ad7566b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"137\" width=\"373\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u8fdb\u884c\u8fd0\u7b97\u5e76\u5c3d\u53ef\u80fd\u7b80\u5316\u5206\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-af3f7cb513883d1fa5dadca23701c19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\\\[2ex]&amp;=\\cfrac{15x^4-24x^2+40x^3-64x-10x^4-40x^3}{25x^4+64-80x^2}\\\\[2ex]&amp;=\\cfrac{5x^4-24x^2-64x}{25x^4-80x^2+64}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"379\" 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-un-cociente\"><\/span>\u89e3\u51b3\u4e86\u5546\u5bfc\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a8\u5bfc\u51fa\u4ee5\u4e0b\u529f\u80fd\u5212\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-e6244d0e6cfcb8c4b82806d40cab93fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\cfrac{9x^2+5x}{6x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"154\" 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-e94071c6dc40cd4a7280be617cdddd3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\cfrac{19}{2x^2-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" 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-214e8c32a9ffb1c37f164935c3ad6bfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\cfrac{8x^3-4x^2+3x}{e^{4x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"202\" 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-a83ff4c06137279870296a80b12b0cec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\cfrac{\\text{cos}(x^2)}{\\text{sen}(6x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"144\" 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-4bed0ff9464adb5897528d5b47ed477c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\cfrac{\\ln(x^3+4)}{\\left(4x^2-3x\\right)^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"174\" style=\"vertical-align: -20px;\"><\/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-74ddf8caa494c9a60dcbfc9d57c90d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f(x)=\\cfrac{\\sqrt{x^2+4x}}{5^{x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"158\" style=\"vertical-align: -13px;\"><\/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-26b0af84dd46ca29727eee97380b4ca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{A) }f'(x)&amp;=\\cfrac{(18x+5)\\cdot 6x^3-(9x^2+5x)\\cdot 18x^2}{\\left(6x^3\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{108x^4+30x^3-162x^4-90x^3}{36x^6}\\\\[1.5ex]&amp;=\\cfrac{-54x^4-60x^3}{36x^6}\\\\[1.5ex]&amp;=\\cfrac{-9x-10}{6x^3}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"225\" width=\"354\" style=\"vertical-align: 0px;\"><\/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-97bee45dee6ebba49cd8a9822ef70308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\cfrac{-19\\cdot 4x}{\\left(2x^2-2\\right)^2}=\\cfrac{-76x}{\\left(2x^2-2\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"273\" style=\"vertical-align: -20px;\"><\/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-11f9c8fda61edb1ce51bd33e022a0a24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp;=\\cfrac{(24x^2-8x+3)e^{4x}-(8x^3-4x^2+3x)\\cdot 4e^{4x}}{\\left(e^{4x}\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{e^{4x}(24x^2-8x+3-32x^3+16x^2-12x)}{e^{8x}}\\\\[1.5ex]&amp;=\\cfrac{-32x^3+40x^2-20x+3}{e^{4x}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"431\" style=\"vertical-align: 0px;\"><\/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-da9da045ccfc03ecc1d9d44e1ea9caee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=\\cfrac{-2x\\text{sen}(x^2)\\cdot\\text{sen}(6x)-\\text{cos}(x^2)\\text{cos}(6x)\\cdot 6}{\\text{sen}^2(6x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"414\" 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-ec87daa1a463bacd5a42a1b16e826449_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) }f'(x)&amp;=\\cfrac{\\cfrac{3x^2}{x^3+4}\\cdot\\left(4x^2-3x\\right)^3-\\ln(x^3+4)\\cdot 3\\left(4x^2-3x\\right)^2\\cdot (8x-3) }{\\left(\\left(4x^2-3x\\right)^3\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{\\cfrac{3x^2}{x^3+4}\\cdot\\left(4x^2-3x\\right)^3-\\ln(x^3+4)\\cdot 3\\left(4x^2-3x\\right)^2\\cdot (8x-3) }{\\left(4x^2-3x\\right)^6}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"170\" width=\"535\" style=\"vertical-align: 0px;\"><\/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-bef2b22482e39cea7e82047c0d9911b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{F) }f'(x)&amp;=\\cfrac{\\cfrac{2x+4}{2\\sqrt{x^2+4x}}\\cdot 5^{x^2} - \\sqrt{x^2+4x}\\cdot 5^{x^2}\\cdot \\ln(5) \\cdot 2x }{\\left(5^{x^2}\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{\\cfrac{2x+4}{2\\sqrt{x^2+4x}}\\cdot 5^{x^2} - \\sqrt{x^2+4x}\\cdot 5^{x^2}\\cdot \\ln(5) \\cdot 2x }{5^{2x^2}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"155\" width=\"424\" style=\"vertical-align: 0px;\"><\/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-derivada-de-un-cociente\"><\/span>\u5546\u7684\u5bfc\u6570\u7684\u6f14\u793a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u6f14\u793a\u9664\u6cd5\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u5bfc\u6570\u7684\u4e00\u822c\u5b9a\u4e49\uff0c\u5373\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\u4e24\u4e2a\u4e0d\u540c\u51fd\u6570\u7684\u9664\u6cd5\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-83357f61a7cd6587a3fd5e5348b056fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=\\cfrac{f(x)}{g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"94\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u90a3\u4e48\uff0c\u5e94\u7528\u6570\u5b66\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-db6545eb9e109966a362acf510f101a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\cfrac{f(x+h)}{g(x+h)}-\\cfrac{f(x)}{g(x)}}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"223\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u7528\u5206\u6570\u7684\u5206\u5b50\u6765\u6c42\u89e3\u5206\u6570\u51cf\u6cd5\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-f9ec617a63f72bd4215ccb2b2998525e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\cfrac{f(x+h)\\cdot g(x)}{g(x+h)\\cdot g(x)}-\\cfrac{f(x)\\cdot g(x+h)}{g(x)\\cdot g(x+h)}}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"347\" style=\"vertical-align: -13px;\"><\/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-f8a9e6382fd7033298df2e7955ccd9fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x)-f(x)\\cdot g(x+h)}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"343\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5728\u65b9\u7a0b\u4e2d\u6dfb\u52a0\u52a0\u6cd5\u548c\u51cf\u6cd5\u9879\u4e0d\u4f1a\u6539\u53d8\u65b9\u7a0b\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-8581512accedfadade2e1bbbeec84855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x)\\color{orange}\\bm{-f(x)\\cdot g(x)}\\color{black}-f(x)\\cdot g(x+h)\\color{orange}\\bm{+f(x)\\cdot g(x)}\\color{black}}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"720\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u63d0\u53d6\u516c\u56e0\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-b8f9b502b411bb77acebc63c00972053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{g(x)\\bigl[f(x+h)-f(x)\\bigr]-f(x)\\bigl[g(x+h)-g(x)\\bigr]}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"457\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u8ba9\u6211\u4eec\u5229\u7528\u5206\u6570\u7684\u6027\u8d28\u5c06<em>h<\/em>\u9879\u4ece\u5206\u6bcd\u79fb\u81f3\u5206\u5b50\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-74338b745f98dd32abeea2df50b88ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{g(x)\\cdot \\cfrac{f(x+h)-f(x)\\cdot g(x)}{h}-f(x)\\cdot\\cfrac{g(x+h)-g(x)}{h}}{g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"503\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u901a\u8fc7\u5e94\u7528\u6781\u9650\u7684\u6027\u8d28\u6765\u53d8\u6362\u65b9\u7a0b\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-a699ddaf78abfcfbd1aa3993b6a0b033_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}\\cfrac{f(x+h)-f(x)\\cdot g(x)}{h}-f(x)\\cdot\\lim_{h \\to 0}\\cfrac{g(x+h)-g(x)}{h}}{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"535\" style=\"vertical-align: -25px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u7684\u6781\u9650\u7cbe\u786e\u5bf9\u5e94\u4e8e\u6bcf\u4e2a\u51fd\u6570\u5bfc\u6570\u7684\u6570\u5b66\u5b9a\u4e49\uff0c\u56e0\u6b64\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-8735d5a5a43fa63c27443c2fe34a1530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot f'(x)-f(x)\\cdot g'(x)}{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"257\" style=\"vertical-align: -25px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u6c42\u89e3\u5206\u6570\u5206\u6bcd\u7684\u6781\u9650\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-1ef05117a36f586b6c8441b829bd4c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot f'(x)-f(x)\\cdot g'(x)}{g(x)\\cdot g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"257\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u7531\u6b64\u8bc1\u660e\u4e86\u4e24\u4e2a\u51fd\u6570\u7684\u5546\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-85517a8cdcfda040b304fbdabe67a5fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"257\" style=\"vertical-align: -23px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u4ece\u4e24\u4e2a\u51fd\u6570\u5bfc\u51fa\u5546\uff08\u6216\u9664\u6cd5\uff09\u3002\u60a8\u5c06\u627e\u5230\u51fd\u6570\u5546\u7684\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u5206\u6b65\u7ec3\u4e60\u6765\u7ec3\u4e60 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e9%99%a4%e5%95%86%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u5546\uff08\u6216\u9664\u6cd5\uff09\u7684\u5bfc\u6570<\/span> \u67e5\u770b\u5168\u6587 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