{"id":392,"date":"2023-07-03T00:18:18","date_gmt":"2023-07-03T00:18:18","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e8%a1%8d%e7%94%9f%e5%93%81\/"},"modified":"2023-07-03T00:18:18","modified_gmt":"2023-07-03T00:18:18","slug":"%e8%a1%8d%e7%94%9f%e5%93%81","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e8%a1%8d%e7%94%9f%e5%93%81\/","title":{"rendered":"\u884d\u751f\u54c1"},"content":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u6240\u6709\u7c7b\u578b\u7684\u51fd\u6570\u3002\u60a8\u5c06\u627e\u5230\u6240\u6709\u5bfc\u6570\u7684\u516c\u5f0f\u4ee5\u53ca\u793a\u4f8b\u548c\u5206\u6b65\u5bfc\u6570\u7ec3\u4e60\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formules-derivees.webp\" alt=\"\u5bfc\u51fa\u516c\u5f0f\" class=\"wp-image-2945\" width=\"226\" height=\"226\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-las-derivadas\"><\/span>\u4ec0\u4e48\u662f\u884d\u751f\u4ea7\u54c1\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5bfc\u6570<\/strong>\u662f\u7528\u4e8e\u7814\u7a76\u51fd\u6570\u7684\u6570\u5b66\u89c4\u5219\u3002\u7279\u522b\u662f\uff0c<strong>\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u7684\u5bfc\u6570<\/strong>\u662f\u6781\u9650\u7684\u7ed3\u679c\uff0c\u8868\u793a\u51fd\u6570\u5728\u8be5\u70b9\u7684\u884c\u4e3a\u3002<\/p>\n<p>\u51fd\u6570\u7684\u5bfc\u6570\u7528\u6487\u53f7<em>&#8216;<\/em>\u8868\u793a\uff0c\u4e5f\u5c31\u662f\u8bf4\u51fd\u6570<em>f'(x)<\/em>\u662f\u51fd\u6570<em>f(x)<\/em>\u7684\u5bfc\u6570\u3002<\/p>\n<p>\u5728\u51e0\u4f55\u4e0a\uff0c\u51fd\u6570\u5728\u4e00\u70b9\u7684\u5bfc\u6570\u7684\u542b\u4e49\u662f\u51fd\u6570\u5728\u8be5\u70b9\u7684\u5207\u7ebf\u7684\u659c\u7387\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equation-de-la-tangente-ligne.webp\" alt=\"\u884d\u751f\u54c1\u7684\u542b\u4e49\" class=\"wp-image-2306\" width=\"392\" height=\"391\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p><strong>\u51fd\u6570\u5bfc\u6570\u7684\u6570\u5b66\u5b9a\u4e49<\/strong>\u5982\u4e0b\uff1a<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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> \u7136\u800c\uff0c\u51fd\u6570\u7684\u5bfc\u6570\u901a\u5e38\u4e0d\u4f7f\u7528\u4e0a\u8ff0\u516c\u5f0f\u8ba1\u7b97\uff0c\u800c\u662f\u6839\u636e\u51fd\u6570\u7684\u7c7b\u578b\u5e94\u7528\u5fae\u5206\u89c4\u5219\u3002\u4e0b\u9762\u89e3\u91ca\u6240\u6709\u7684\u63a8\u5bfc\u516c\u5f0f\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-las-derivadas\"><\/span>\u5bfc\u51fa\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e86\u89e3\u5bfc\u6570\u7684\u5b9a\u4e49\u540e\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5b83\u4eec\u662f\u5982\u4f55\u5236\u4f5c\u7684\uff0c\u5e76\u901a\u8fc7\u793a\u4f8b\u89e3\u91ca\u6bcf\u79cd\u7c7b\u578b\u7684\u5bfc\u6570\u3002\u8fd9\u7bc7\u6587\u7ae0\u7684\u76ee\u7684\u662f\u8ba9\u4f60\u66f4\u597d\u5730\u7406\u89e3\u5bfc\u6570\u7684\u6982\u5ff5\uff0c\u6240\u4ee5\u5982\u679c\u4f60\u6700\u7ec8\u5bf9\u51fd\u6570\u662f\u5982\u4f55\u63a8\u5bfc\u6709\u4efb\u4f55\u7591\u95ee\uff0c\u53ef\u4ee5\u5728\u8bc4\u8bba\u4e2d\u8be2\u95ee\u6211\u4eec\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-constante\"><\/span>\u7531\u5e38\u6570\u5bfc\u51fa<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u65e0\u8bba<strong>\u5e38\u6570\u7684\u503c\u5982\u4f55\uff0c\u5e38\u6570\u7684\u5bfc\u6570<\/strong>\u59cb\u7ec8\u4e3a\u96f6\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-c7bd8f1aee171f251c313218820e22f0_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=k \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=0 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u6c42\u5e38\u6570\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u4e0d\u9700\u8981\u505a\u4efb\u4f55\u6570\u5b66\u8fd0\u7b97\uff0c\u53ea\u9700\u5bfc\u6570\u4e3a\u96f6\u5373\u53ef\u3002<\/p>\n<p>\u770b\u770b\u4e0b\u9762\u5e38\u6570\u5bfc\u6570\u7684\u5b9e\u9645\u4f8b\u5b50\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-561a1b2c2b0347c0cb38ed7565e46fa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=3 \\qquad \\longrightarrow\\qquad f'(x)=0\\\\[3ex]g(x)=-5 \\qquad \\longrightarrow\\qquad g'(x)=0\\\\[3ex]h(x)=291 \\qquad \\longrightarrow\\qquad h'(x)=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"265\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-lineal\"><\/span>\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570<\/strong>\u662f\u4e00\u6b21\u9879\u7684\u7cfb\u6570\uff0c\u4e5f\u5c31\u662f\u8bf4\u7ebf\u6027\u51fd\u6570\u7684\u5bfc\u6570<em>f(x)=Ax+B<\/em>\u7b49\u4e8e<em>A<\/em><\/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-c55a9a25283e37ab61dc79856ee92a11_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=Ax+B\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=A \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u770b\u4e00\u4e0b\u4ee5\u4e0b\u793a\u4f8b\uff0c\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u6b64\u7c7b\u51fd\u6570\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-53d0d8c8814ef6884b442c3c50cce8a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=3x-1\\quad\\longrightarrow\\quad f'(x)=3\\\\[3ex]f(x)=5x\\quad\\longrightarrow\\quad f'(x)=5\\\\[3ex] f(x)=-2x+9\\quad\\longrightarrow\\quad f'(x)=-2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"280\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-potencia\"><\/span>\u6e90\u4e8e\u4e00\u79cd\u529b\u91cf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5e42\u6216\u52bf\u51fd\u6570\u7684\u5bfc\u6570<\/strong>\u662f\u5e42\u7684\u6307\u6570\u4e58\u4ee5\u6307\u6570\u8d1f 1 \u7684\u5e95\u6570\u7684\u4e58\u79ef\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-1e7df9c631129b040e262f67f36b41be_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=x^k \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=k\\cdot x^{k-1} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u5bfc\u51fa\u5e42\uff0c\u53ea\u9700\u5c06\u51fd\u6570\u4e58\u4ee5\u6307\u6570\uff0c\u7136\u540e\u4ece\u6307\u6570\u4e2d\u51cf\u53bb\u4e00\u4e2a\u5355\u4f4d\u5373\u53ef\u3002<\/p>\n<p>\u4f8b\u5982\uff0cx \u4e09\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-0c0dd56d2e4a99c896f5e035d51f80be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=3\\cdot x^{3-1}=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u60a8\u53ef\u4ee5\u5728\u8fd9\u91cc\u7ec3\u4e60\u6b64\u7c7b\u5bfc\u6570\u7684\u7ec3\u4e60\uff08\u4ee5\u53ca\u66f4\u56f0\u96be\u7684\u7ec3\u4e60\uff09\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\/\u529f\u7387\u52bf\u51fd\u6570\u7684\u5bfc\u6570\/\">\u5df2\u89e3\u51b3\u5e42\u5bfc\u6570\u7684\u7ec3\u4e60<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-raiz\"><\/span>\u6e90\u4e8e\u4e00\u4e2a\u6839<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><meta charset=\"utf-8\"><strong>\u6839\u6216\u65e0\u7406\u51fd\u6570\u7684\u5bfc\u6570<\/strong>\u7b49\u4e8e 1 \u9664\u4ee5\u6839\u7684\u7d22\u5f15\u4e58\u4ee5\u540c\u4e00\u6839\u7684\u4e58\u79ef\u518d\u4ece\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-8b8e85735674a043d4fb2c448038ceb8_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=1pt, boxsep=1.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      f(x)=\\sqrt[n]{x}\\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad f'(x)=\\cfrac{1}{n\\sqrt[n]{x^{n-1}}} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f5c\u4e3a\u793a\u4f8b\uff0c\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u770b\u5230\u5df2\u6c42\u89e3\u7684 x \u5e73\u65b9\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-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<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6839\u5f0f\u65e0\u7406\u6839\u51fd\u6570\u7684\u5bfc\u6570\/\">\u6839\u7684\u5bfc\u6570\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-exponencial\"><\/span>\u6307\u6570\u51fd\u6570\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u6307\u6570\u51fd\u6570\u7684\u5bfc\u6570<\/strong>\u53d6\u51b3\u4e8e\u5e95\u6570\u662f\u6570\u5b57<em>e<\/em>\u8fd8\u662f\u5176\u4ed6\u6570\u5b57\u3002\u56e0\u6b64\uff0c\u6709\u4e24\u4e2a\u516c\u5f0f\u53ef\u4ee5\u5bfc\u51fa\u6b64\u7c7b\u51fd\u6570\uff0c\u5e76\u4e14\u60a8\u5fc5\u987b\u4f7f\u7528\u6839\u636e\u529f\u7387\u57fa\u7840\u5bf9\u5e94\u7684\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-c21e61c79c41a4f27d53a41495521bdd_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=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=a^x \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=a^x\\cdot \\ln(a)\\\\[3ex] f(x)=e^x \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=e^x \\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u6b64\u7c7b\u51fd\u6570\u7684\u4e24\u4e2a\u5df2\u6c42\u89e3\u5bfc\u6570\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-90bd19942de37daaf7af04179eaf5e91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=7^{x} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=7^x\\cdot \\ln(7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-71dd62c13ea22caa62fb0e8af338fbdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=e^{x} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=e^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"312\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\u5bfc\u6570\u7684\u5df2\u89e3\u7b54\u7ec3\u4e60<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-una-funcion-logaritmica\"><\/span>\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570<\/strong>\u53d6\u51b3\u4e8e\u5bf9\u6570\u7684\u5e95\u6570\uff0c\u56e0\u4e3a\u5982\u679c\u5bf9\u6570\u662f\u81ea\u7136\u6570\uff0c\u5219\u5fc5\u987b\u5e94\u7528\u516c\u5f0f\u6765\u6c42\u5bfc\u6570\uff0c\u5982\u679c\u5bf9\u6570\u6709\u53e6\u4e00\u4e2a\u6570\u5b57\u4f5c\u4e3a\u5e95\u6570\uff0c\u5219\u5fc5\u987b\u4f7f\u7528\u53e6\u4e00\u4e2a\u89c4\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-d384075ba6ad6dcfaf82949d33ad397b_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=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=\\ln(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x}\\\\[3ex] f(x)=\\log_a(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(a)}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0cx \u4ee5\u4e09\u4e3a\u5e95\u7684\u5bf9\u6570\u7684\u5bfc\u6570\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-e61ac2c2f66f8b05dce8760bdec17d09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_3(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/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\u5bfc\u6570\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60<\/a><\/span><\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivadas-trigonometricas\"><\/span>\u4e09\u89d2\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u4e09\u89d2\u5bfc\u6570\u7684\u4e09\u79cd\u4e3b\u8981\u5f62\u5f0f<\/strong>\u662f\u6b63\u5f26\u51fd\u6570\u3001\u4f59\u5f26\u51fd\u6570\u548c\u6b63\u5207\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u5176\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-a9e9d0157c2b1eb994571ba96aae4f26_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=1pt, boxsep=1.8mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}f(x)=\\text{sen}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x)\\\\[2.5ex] f(x)=\\text{cos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(x)\\\\[1.1ex]f(x)=\\text{tan}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{\\text{cos}^2(x)}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u4e09\u89d2\u51fd\u6570\u6709\u51e0\u79cd\u7c7b\u578b\uff0c\u4f8b\u5982\u6b63\u5272\u3001\u4f59\u5272\u3001\u4f59\u5207\u3001\u53cc\u66f2\u4e09\u89d2\u51fd\u6570\u3001\u53cd\u4e09\u89d2\u51fd\u6570\u7b49\u3002\u4f46\u6700\u5e38\u7528\u7684\u6f02\u79fb\u89c4\u5219\u662f\u4ee5\u4e0a\u4e09\u4e2a\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"reglas-de-derivacion\"><\/span>\u63a8\u8350\u89c4\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5f53\u6211\u4eec\u8fdb\u884c\u51fd\u6570\u8fd0\u7b97\u65f6\uff0c\u5bfc\u6570\u7684\u6c42\u89e3\u65b9\u5f0f\u6709\u6240\u4e0d\u540c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528<strong>\u5fae\u5206\u89c4\u5219<\/strong>\uff0c\u5b83\u5141\u8bb8\u6211\u4eec\u5bfc\u51fa\u51fd\u6570\u7684\u52a0\u6cd5\u3001\u51cf\u6cd5\u3001\u4e58\u6cd5\u548c\u9664\u6cd5\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-ba4f3225344df68c84b4437ecb0c7536_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=1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{l}z(x)=f(x)\\pm g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\pm g'(x)\\\\[4ex] z(x)=f(x)\\cdot g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\cdot g(x)+f(x)\\cdot g'(x)\\\\[4ex]z(x)=\\cfrac{f(x)}{g(x)} \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7528\u8fd0\u7b97\u6c42\u89e3\u5bfc\u6570\uff0c\u4e0d\u4ec5\u9700\u8981\u5e94\u7528\u5bfc\u6570\u89c4\u5219\uff0c\u8fd8\u9700\u8981\u4f7f\u7528\u6bcf\u79cd\u5bfc\u6570\u7684\u516c\u5f0f\u3002<\/p>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u4e86\u89e3\u5982\u4f55\u627e\u5230\u6b64\u7c7b\u5bfc\u6570\uff0c\u6211\u4eec\u5c06\u89e3\u51b3\u4ee5\u4e0b\u51e0\u4e2a\u7ec3\u4e60\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li><span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">\u603b\u548c\u7684\u5bfc\u6570\uff1a<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-efca27bad0818b86e6e42ee15a31ed6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3x^2+5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"125\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-8a8dcfca37df757df3fd79292ead67b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=6x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u4e3a\u4e86\u6c42\u89e3\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u5c06\u5e42\u5bfc\u6570\u7684\u516c\u5f0f\u5e94\u7528\u4e8e\u603b\u548c\u7684\u6bcf\u4e00\u9879\u3002<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li><span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">\u6e90\u81ea\u4ea7\u54c1\uff1a<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-8c539c8db8dbf532a639e09af47a583a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=4^{x}\\cdot \\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e58\u79ef\u7b2c\u4e00\u9879\u7684\u5bfc\u6570\u662f 4 <sup>x<\/sup> ln(4)\uff0c\u6b63\u5f26\u7684\u5bfc\u6570\u662f\u4f59\u5f26\u3002\u6240\u4ee5\u4e58\u6cd5\u7684\u5bfc\u6570\u662f\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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-5829940bb4219334d7e238b40a19794e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=4^{x}\\cdot \\ln (4) \\cdot \\text{sen}(x) +4^{x}\\cdot \\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li><span style=\"color:#101010;font-weight: normal;\"><u style=\"text-decoration-color:#FF9B28;\">\u5546\u7684\u5bfc\u6570\uff1a<\/u><\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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>\u5728\u5206\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u591a\u9879\u5f0f\uff0c\u56e0\u6b64\u8981\u5f97\u5230\u5bfc\u6570\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u5546\u7684\u5bfc\u6570\u516c\u5f0f\u3001\u52a0\uff08\u6216\u51cf\uff09\u7684\u5bfc\u6570\u516c\u5f0f\u4ee5\u53ca\u6709\u6743\u529b\uff1a <\/p>\n<p class=\"has-text-align-center\"><meta charset=\"utf-8\"><\/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=\"regla-de-la-cadena\"><\/span>\u94fe\u5f0f\u6cd5\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><meta charset=\"utf-8\"><strong>\u94fe\u5f0f\u6cd5\u5219<\/strong>\u662f\u7528\u4e8e\u5bfc\u51fa\u590d\u5408\u51fd\u6570\u7684\u516c\u5f0f\u3002\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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-662d8c44c904e83267bbca5f968ca546_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=1pt, boxsep=1.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      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) \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5bfc\u6570\u7684\u6982\u5ff5\u901a\u5e38\u6bd4\u8f83\u96be\u4ee5\u7406\u89e3\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f5c\u4e3a\u793a\u4f8b\u9010\u6b65\u89e3\u51b3\u4e00\u4e2a\u7ec3\u4e60\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-c1863b1f92befa398b5c8692d239abf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5b9e\u9645\u4e0a\uff0c\u5b83\u662f\u51fd\u6570\u7684\u7ec4\u5408\uff0c\u56e0\u4e3a\u6b63\u5f26\u51fd\u6570\u4e2d\u6709\u51fd\u6570 x <sup>3<\/sup> \uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\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\u5177\u6709\u4e0e\u6b63\u5f26\u76f8\u540c\u53c2\u6570\u7684\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-2046d85a1440fe95dccc4d8bb553e2f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\\bigl(g(x)\\bigr)=\\text{sen}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'\\bigl(g(x)\\bigr)=\\text{cos}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"441\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u4f7f\u7528\u5e42\u5bfc\u6570\u516c\u5f0f\u8ba1\u7b97 x <sup>3<\/sup>\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-1d045f948b3519322ae6771bd4497d70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)=x^3\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} g'(x)=3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"320\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6574\u6570\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-ab755de02fa9196320c59676d77cd2e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x^3) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{cos}(x^3)\\cdot 3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"430\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\/\u6d3e\u751f\u89c4\u5219\u94fe\/\">\u7528\u94fe\u5f0f\u6cd5\u5219\u89e3\u51b3\u5bfc\u6570\u7ec3\u4e60<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivabilidad-de-una-funcion\"><\/span>\u51fd\u6570\u7684\u53ef\u5fae\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51fd\u6570\u5728\u4e00\u70b9\u7684\u8fde\u7eed\u6027\u548c\u53ef\u5bfc\u6027<\/strong>\u5173\u7cfb\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u51fd\u6570\u5728\u4e00\u70b9\u53ef\u5fae\uff0c\u5219\u8be5\u51fd\u6570\u5728\u8be5\u70b9\u8fde\u7eed\u3002<\/li>\n<li>\u5982\u679c\u51fd\u6570\u5728\u4e00\u70b9\u4e0d\u8fde\u7eed\uff0c\u90a3\u4e48\u5b83\u5728\u8be5\u70b9\u4e5f\u662f\u4e0d\u53ef\u5fae\u7684\u3002<\/li>\n<\/ul>\n<p>\u7136\u800c\uff0c\u8be5\u5b9a\u7406\u7684\u9006\u547d\u9898\u662f\u9519\u8bef\u7684\uff0c\u5373\u4ec5\u4ec5\u56e0\u4e3a\u51fd\u6570\u5728\u4e00\u70b9\u8fde\u7eed\u5e76\u4e0d\u610f\u5473\u7740\u5b83\u5728\u8be5\u70b9\u603b\u662f\u53ef\u5fae\u7684\u3002<\/p>\n<p>\u60a8\u8fd8\u53ef\u4ee5\u67e5\u770b\u51fd\u6570\u5728\u5176\u56fe\u4e2d\u7684\u67d0\u4e2a\u70b9\u662f\u5426\u53ef\u5fae\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u662f<strong>\u5e73\u6ed1\u70b9\uff0c<\/strong>\u5219\u51fd\u6570\u5728\u8be5\u70b9\u53ef\u5fae\u3002<\/li>\n<li>\u5982\u679c\u662f<strong>\u89d2\u70b9\uff0c<\/strong>\u5219\u51fd\u6570\u5728\u8be5\u70b9\u8fde\u7eed\u4f46\u4e0d\u53ef\u5fae\u3002 <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-3\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\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\/exercices-resolus-pour-representer-une-fonction-quadratique-incomplete.webp\" alt=\"\" class=\"wp-image-140\" width=\"250\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> x=0 \u5904\u7684<span style=\"color:#1976d2;\"><strong>\u5e73\u6ed1\u70b9<\/strong><\/span>\uff1a<br \/>\u6b64\u65f6\u51fd\u6570\u8fde\u7eed\u4e14\u53ef\u5fae\u3002 <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\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\/comment-representer-graphiquement-une-fonction-avec-valeur-absolue.webp\" alt=\"\" class=\"wp-image-230\" width=\"286\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center\"> x=2 \u5904\u7684<span style=\"color:#1976d2;\"><strong>\u659c\u70b9<\/strong><\/span>\uff1a<br \/>\u51fd\u6570\u8fde\u7eed\u4f46\u6b64\u65f6\u4e0d\u53ef\u5fae\u3002<\/p>\n<\/div>\n<\/div>\n<p>\u60a8\u8fd8\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u8be5\u70b9\u7684<strong>\u6a2a\u5411\u5bfc\u6570<\/strong>\u6765\u5224\u65ad\u5206\u6bb5\u51fd\u6570\u5728\u8be5\u70b9\u662f\u5426\u53ef\u5fae\uff1a <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 20px; border-radius:20px;\">\n<ul style=\"color:#64B5F6; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u67d0\u70b9\u7684\u4fa7\u5bfc\u6570\u4e0d\u76f8\u7b49\uff0c\u5219\u51fd\u6570\u5728\u8be5\u70b9\u4e0d\u53ef\u5fae\uff1a<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97c60c64dc01a7e0a9084313d15b0886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x_o^-) \\neq f'(x_o^+) \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5b83\u4e0d\u53ef\u5fae\u5206\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67ab403a6241009b92035b251f86c88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_o\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<ul style=\"color:#64B5F6; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u5982\u679c\u67d0\u70b9\u7684\u4fa7\u5bfc\u6570\u91cd\u5408\uff0c\u5219\u51fd\u6570\u5728\u8be5\u70b9\u53ef\u5fae\uff1a<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f9477828318b9e6392465762f831642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x_o^-) = f'(x_o^+) \\ \\longrightarrow\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u7684\uff0c\u5b83\u53ef\u4ee5\u5bfc\u51fa<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-67ab403a6241009b92035b251f86c88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_o\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u8ba1\u7b97\u5728\u67d0\u4e00\u70b9\u5206\u6bb5\u5b9a\u4e49\u7684\u51fd\u6570\u7684\u5bfc\u6570\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u7814\u7a76\u4ee5\u4e0b\u5206\u6bb5\u51fd\u6570\u5728\u70b9 x=2 \u5904\u7684\u8fde\u7eed\u6027\u548c\u53ef\u5fae\u6027\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a98eee72521c68fd394eb6209a7d0a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=  \\left\\{ \\begin{array}{lcl} 3x^2-6x &amp; \\text{si} &amp;  x<2 \\\\[2ex] 6\\ln (x-1) &amp; \\text{si} &amp; x\\geq 2 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"249\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e24\u6bb5\u51fd\u6570\u5728\u5404\u81ea\u533a\u95f4\u5185\u8fde\u7eed\uff0c\u4f46\u9700\u8981\u68c0\u67e5\u51fd\u6570\u5728\u4e34\u754c\u70b9x=2\u5904\u662f\u5426\u8fde\u7eed\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u6c42\u89e3\u51fd\u6570\u5728\u8be5\u70b9\u7684\u6a2a\u5411\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-dad5bcb0055431aa87a67068c04d2ce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x\\to 2^-} f(x) = \\lim\\limits_{x\\to 2^-} \\bigl(3x^2-6x\\bigr) = 3\\cdot2^2-6\\cdot2=12-12=\\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"449\" style=\"vertical-align: -14px;\"><\/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-31e1ba2ea2c5fd9fa86e5cefed0e5535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lim\\limits_{x\\to 2^+} f(x) = \\lim\\limits_{x\\to 2^+} 6\\ln (x-1) = 6\\ln (2-1)=6 \\ln 1=6 \\cdot 0= \\bm{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"474\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u4e34\u754c\u70b9\u5904\u7684\u6a2a\u5411\u6781\u9650\u7ed9\u4e86\u6211\u4eec\u76f8\u540c\u7684\u7ed3\u679c\uff0c\u56e0\u6b64\u51fd\u6570\u5728 x=2 \u70b9\u5904\u8fde\u7eed\u3002<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u51fd\u6570\u5728 x=2 \u5904\u8fde\u7eed\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u51fd\u6570\u5728\u6b64\u65f6\u7684\u53ef\u5fae\u6027\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u5206\u6bb5\u5b9a\u4e49\u51fd\u6570\u7684<strong>\u4fa7\u5bfc\u6570<\/strong>\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-3709995609d0f69f382ff651e397c00a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)= \\left\\{ \\begin{array}{lcl} 6x-6 &amp; \\text{si} &amp;  x<2 \\\\[2ex] \\cfrac{6}{x-1} &amp; \\text{si} &amp; x\\geq 2 \\end{array} \\right.\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8bc4\u4f30\u4e34\u754c\u70b9\u5904\u7684\u6bcf\u4e2a\u4fa7\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-ca27189960575c1151402d040bfa76f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^-)=6\\cdot2-6=12-6 = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"239\" 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-058310a16d7d545ea56e99517845842b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^+)=\\cfrac{6}{2-1} = \\cfrac{6}{1} = \\bm{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4e24\u4e2a\u6a2a\u5411\u5bfc\u6570\u7ed9\u51fa\u4e86\u76f8\u540c\u7684\u7ed3\u679c\uff0c\u56e0\u6b64\u51fd\u6570\u5728 x=2 \u5904\u53ef\u5fae\uff0c\u5bfc\u6570\u503c\u4e3a 6\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-aadf046f27916c46f0a302d6e0c34113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2^-) = f'(2^+) = 6 \\ \\longrightarrow \\ \\bm{f'(2) = 6}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"275\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u6a2a\u5411\u5bfc\u6570\u7ed9\u4e86\u6211\u4eec\u4e0d\u540c\u7684\u7ed3\u679c\uff0c\u5219\u610f\u5473\u7740\u8be5\u51fd\u6570\u5728 x=2 \u5904\u4e0d\u53ef\u5fae\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6b64\u65f6\u7684\u5bfc\u6570\u5c06\u4e0d\u5b58\u5728\u3002<\/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\/\u51fd\u6570\u7684\u53ef\u5fae\u6027\/\">\u5df2\u89e3\u51b3\u51fd\u6570\u53ef\u5fae\u5206\u7684\u7ec3\u4e60<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u6240\u6709\u7c7b\u578b\u7684\u51fd\u6570\u3002\u60a8\u5c06\u627e\u5230\u6240\u6709\u5bfc\u6570\u7684\u516c\u5f0f\u4ee5\u53ca\u793a\u4f8b\u548c\u5206\u6b65\u5bfc\u6570\u7ec3\u4e60\u3002 \u4ec0\u4e48\u662f\u884d\u751f\u4ea7\u54c1\uff1f \u5bfc\u6570\u662f\u7528 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e8%a1%8d%e7%94%9f%e5%93%81\/\"> <span class=\"screen-reader-text\">\u884d\u751f\u54c1<\/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-392","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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