{"id":372,"date":"2023-07-03T18:53:21","date_gmt":"2023-07-03T18:53:21","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%af%b9%e6%95%b0%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0-neperian-%e8%87%aa%e7%84%b6%e5%af%b9%e6%95%b0\/"},"modified":"2023-07-03T18:53:21","modified_gmt":"2023-07-03T18:53:21","slug":"%e5%af%b9%e6%95%b0%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0-neperian-%e8%87%aa%e7%84%b6%e5%af%b9%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%af%b9%e6%95%b0%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0-neperian-%e8%87%aa%e7%84%b6%e5%af%b9%e6%95%b0\/","title":{"rendered":"\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u6c42\u89e3\u4efb\u4f55\u5e95\u6570\uff08\u516c\u5f0f\uff09\u4e2d\u7684\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u9010\u6b65\u7ec3\u4e60\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u3002<\/p>\n<p><strong>\u5bf9\u6570\u51fd\u6570\u7684\u9664\u6cd5\u516c\u5f0f\u53d6\u51b3\u4e8e\u5bf9\u6570\u662f\u81ea\u7136\u5bf9\u6570\uff08\u4ee5 e \u4e3a\u5e95\uff09\u8fd8\u662f\u5176\u4ed6\u5e95\u6570<\/strong>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u5c06\u8fd9\u4e24\u4e2a\u516c\u5f0f\u5206\u522b\u770b\u4e00\u4e0b\uff0c\u5e76\u9488\u5bf9\u6bcf\u79cd\u60c5\u51b5\u4e3e\u4f8b\u8bf4\u660e\uff0c\u7136\u540e\u6211\u4eec\u5c06\u5bf9\u8fd9\u4e24\u4e2a\u89c4\u5219\u8fdb\u884c\u603b\u7ed3\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-un-logaritmo-natural-o-neperiano\"><\/span>\u81ea\u7136\u6216\u81ea\u7136\u5bf9\u6570\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u81ea\u7136\u5bf9\u6570\uff08\u6216\u81ea\u7136\u5bf9\u6570\uff09\u7684\u5bfc\u6570\u662f\u5bf9\u6570\u81ea\u53d8\u91cf\u7684\u5bfc\u6570\u9664\u4ee5\u81ea\u53d8\u91cf\u51fd\u6570\u7684\u5546\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-491d95a8a33d226da4fc5d62a8e70f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"335\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u5982\u679c\u5bf9\u6570\u5185\u90e8\u7684\u51fd\u6570\u662f\u6052\u7b49\u51fd\u6570\uff0c\u5219\u5bfc\u6570\u7684\u5206\u5b50\u4e2d\u4fdd\u7559 1\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-1519db0b90e430fab54b04113c435118_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"331\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u770b\u4e0b\u9762\u7684\u4f8b\u5b50\uff0c\u5176\u4e2d\u6c42\u89e3 3x \u81ea\u7136\u5bf9\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-420e2f2cb107eb22019157bcb76c5645_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(3x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{3}{3x}=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"384\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u81ea\u7136\u5bf9\u6570\u662f\u4ee5\u6570\u5b57 e\uff08\u6b27\u62c9\u6570\uff09\u4e3a\u5e95\u7684\u5bf9\u6570\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-d5698ad2315473c75950453c15326f81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ln(x)=\\log_e(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-un-logaritmo-en-base-a\"><\/span>\u57fa\u4e8e\u5bf9\u6570\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5bf9\u6570\u5bf9\u4efb\u4f55\u5e95\u6570\u7684\u5bfc\u6570\u7b49\u4e8e 1 \u9664\u4ee5 x \u4e58\u4ee5\u539f\u59cb\u5bf9\u6570\u5e95\u6570\u7684\u81ea\u7136\u5bf9\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-8b37542882d2bccf84707a3341af5813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{x\\cdot\\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\uff0c\u5219\u5bf9\u6570\u5bfc\u6570\u89c4\u5219\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-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0cx \u5e73\u65b9\u4ee5 2 \u4e3a\u5e95\u7684\u5bf9\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-e934db01ce50b0ef6f597d5952637cfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_2(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{x^2\\cdot\\ln(2)}=\\cfrac{2}{x\\ln(2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"488\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-funcion-logaritmica\"><\/span>\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230\u5bf9\u6570\u5bfc\u6570\u7684\u5b9a\u4e49\u53ca\u5176\u4e24\u79cd\u53ef\u80fd\u7684\u53d8\u4f53\uff0c\u8fd9\u91cc\u603b\u7ed3\u4e86\u8fd9\u4e24\u4e2a\u516c\u5f0f\uff0c\u4ee5\u4fbf\u60a8\u66f4\u5bb9\u6613\u8bb0\u4f4f\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\/fonction-logarithmique-derivee.webp\" alt=\"\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\" class=\"wp-image-1842\" width=\"395\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-de-funciones-logaritmicas\"><\/span>\u89e3\u51b3\u4e86\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u63a8\u5bfc\u4ee5\u4e0b\u5bf9\u6570\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-8118283c3444e6c13b9aefdf0d8a11aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log(3x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9700\u8981\u6c42\u89e3\u5341\u8fdb\u5236\u5bf9\u6570\u7684\u5bfc\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u4ee5 10 \u4e3a\u5e95\u7684\u5bf9\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-f340fe2c5f62e4f0c4499aca10845cf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log(3x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{6x}{3x^2\\cdot \\ln(10)}=\\cfrac{2}{x \\ln(10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"516\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8bf7\u8bb0\u4f4f\uff0c\u5982\u679c\u5bf9\u6570\u6ca1\u6709\u5e95\u6570\uff0c\u5219\u610f\u5473\u7740\u5b83\u7684\u5e95\u6570\u662f 10\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u63a8\u5bfc\u4ee5\u4e0b\u81ea\u7136\uff08\u6216\u81ea\u7136\uff09\u5bf9\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a44fc37965c07092cdfa5cb2679a8b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln\\left(x^3+4x^2\\right)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"165\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u672c\u9898\u4e2d\u7684\u51fd\u6570\u662f\u81ea\u7136\u5bf9\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u4f7f\u7528\u4ee5\u4e0b\u89c4\u5219\u6765\u63a8\u5bfc\u5bf9\u6570\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-491d95a8a33d226da4fc5d62a8e70f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"335\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u81ea\u7136\u5bf9\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-fc06150c0093afdd84076e69171b7d38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{5\\left(x^3+4x^2\\right)^4\\cdot (3x^2+8x)}{\\left(x^3+4x^2\\right)^5}\\\\[2ex] &amp;=\\cfrac{5\\cdot (3x^2+8x)}{x^3+4x^2}\\\\[2ex] &amp;=\\cfrac{15x^2+40x}{x^3+4x^2}\\\\[2ex] &amp;=\\cfrac{15x+40}{x^2+4x}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"245\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u5bfc\u51fa\u4ee5\u4e0b\u5bf9\u6570\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5682f4fd6180c07879cfe9fb6a4b2583_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_7(x^5+7x^2-3x+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"239\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u672c\u7ec3\u4e60\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u5bfc\u51fa\u4ee5 7 \u4e3a\u5e95\u7684\u5bf9\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5bf9\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-182fbf09950c4930013d2f863888bdd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{5x^4+14x-3}{(x^5+7x^2-3x+1)\\cdot \\ln(7)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"267\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u6c42\u4ee5\u4e0b\u5bf9\u6570\u51fd\u6570\u4e0e\u5206\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-218d7543ba82562bbf91b5f4e0ca3f1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\log_4\\left(\\frac{5x}{8x^2-1}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u6c42\u89e3\u5bf9\u6570\u5bfc\u6570\uff0c\u6211\u4eec\u9996\u5148\u53ef\u4ee5\u5e94\u7528\u5bf9\u6570\u7684\u6027\u8d28\u6765\u7b80\u5316\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-2d0cedfe8d0bd4de138099938b10e39f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_4(5x)-\\log_4(8x^2-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"244\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u5bf9\u6570\u5bfc\u6570\u516c\u5f0f\u4e24\u6b21\uff0c\u4f46\u4e24\u6b21\u5bfc\u6570\u90fd\u66f4\u5bb9\u6613\u8ba1\u7b97\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-2fac5d7501d02d27d74a95272a64e756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\log_a(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u\\cdot \\ln(a)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"397\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7efc\u4e0a\u6240\u8ff0\uff0c\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-85874bff9f3259727a78b50aece1f1e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{5}{5x\\cdot \\ln(4)}-\\cfrac{16x}{(8x^2-1)\\cdot \\ln(4)}\\\\[2ex]&amp;=\\cfrac{1}{x\\ln(4)}-\\cfrac{16x}{(8x^2-1)\\ln(4)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"111\" width=\"279\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u5bf9\u6570\u51fd\u6570\u7684\u4e00\u6839\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-9518b9623edc80e9f5de230edb5e573c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln\\left(\\sqrt[4]{\\text{cos}(9x)}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"170\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u9996\u5148\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u5bf9\u6570\u7684\u5c5e\u6027\u6765\u7b80\u5316\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-95cc0f73a05b0cde647035b17d0fed60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln\\left(\\text{cos}(9x)\\right)^{\\frac{1}{4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"154\" 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-fac1c4306bdc844dc069a28c995e5dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{1}{4}\\ln\\left(\\text{cos}(9x)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"161\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u4ece\u51fd\u6570\u4e2d\u5220\u9664\u4e86\u6839\u5f0f\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u81ea\u7136\u6216\u81ea\u7136\u5bf9\u6570\u7684\u5bfc\u6570\u89c4\u5219\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-491d95a8a33d226da4fc5d62a8e70f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\ln(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{u}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"335\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u590d\u5408\u5bf9\u6570\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-440b871bd7321bb0121db9a588adde6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)&amp;=\\cfrac{1}{4}\\cdot \\cfrac{-\\text{sen}(9x)\\cdot 9}{\\text{cos}(9x)}=\\cfrac{-9\\text{sen}(9x)}{4\\text{cos}(9x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"304\" style=\"vertical-align: -17px;\"><\/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\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u6c42\u89e3\u4efb\u4f55\u5e95\u6570\uff08\u516c\u5f0f\uff09\u4e2d\u7684\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u9010\u6b65\u7ec3\u4e60\u5bf9\u6570\u51fd\u6570\u7684\u5bfc\u6570\u3002 \u5bf9\u6570\u51fd\u6570\u7684 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%af%b9%e6%95%b0%e5%87%bd%e6%95%b0%e7%9a%84%e5%af%bc%e6%95%b0-neperian-%e8%87%aa%e7%84%b6%e5%af%b9%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u5bf9\u6570\u51fd\u6570\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-372","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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