{"id":31,"date":"2023-09-17T11:02:40","date_gmt":"2023-09-17T11:02:40","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%88%87%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-09-17T11:02:40","modified_gmt":"2023-09-17T11:02:40","slug":"%e5%88%87%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%88%87%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u5207\u7ebf\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u6b63\u5207\u51fd\u6570\u662f\u5982\u4f55\u5bfc\u51fa\u7684\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5207\u7ebf\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u6211\u4eec\u8fd8\u6f14\u793a\u4e86\u6b63\u5207\u5bfc\u6570\u516c\u5f0f\u5e76\u5411\u60a8\u5c55\u793a\u53cd\u6b63\u5207\u5bfc\u6570\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-de-la-tangente\"><\/span>\u5207\u7ebf\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>x \u7684\u6b63\u5207\u503c\u5bf9 x \u7684\u4f59\u5f26\u5e73\u65b9\u7684\u5bfc\u6570\u7b49\u4e8e 1\u3002<\/strong> x \u7684\u6b63\u5207\u7684\u5bfc\u6570\u4e5f\u7b49\u4e8e x \u7684\u6b63\u5272\u7684\u5e73\u65b9\uff0c1 \u52a0\u4e0a x \u7684\u6b63\u5207\u7684\u5e73\u65b9\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-dfb81626a982a908c4e517b1ecb748e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{tan}(x)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=\\cfrac{1}{\\text{cos}^2(x)}=\\text{sec}^2(x)=1+\\text{tan}^2(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"308\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u6709\u8868\u8fbe\u5f0f\u90fd\u662f\u7b49\u4ef7\u7684\uff0c\u56e0\u6b64\u6b63\u5207\u51fd\u6570\u5177\u6709\u4e09\u4e2a\u53ef\u80fd\u7684\u516c\u5f0f\u6765\u5bfc\u51fa\u5b83\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u5728\u6b63\u5207\u53c2\u6570\u4e2d\u6211\u4eec\u6709\u4e00\u4e2a\u4e0e x \u4e0d\u540c\u7684\u51fd\u6570\uff08\u6211\u4eec\u79f0\u4e4b\u4e3a u\uff09\u65f6\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u3002\u56e0\u6b64 u \u7684\u6b63\u5207\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-1ad272ab857ecf57ebc79e68a4370fc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{tan}(u)\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\color{black}\\\\ f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}=\\text{sec}^2(u)\\cdot u'=\\left(1+\\text{tan}^2(u)\\right)\\cdot u'\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"380\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u6b63\u5207\u5bfc\u6570\u89c4\u5219\u53ef\u4ee5\u6982\u62ec\u4e3a\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/derivee-de-la-tangente.webp\" alt=\"\u6b63\u5207\u5bfc\u6570\" class=\"wp-image-1929\" width=\"418\" height=\"365\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-tangente\"><\/span>\u6b63\u5207\u5bfc\u6570\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u6b63\u5207\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u6c42\u89e3\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u5982\u4f55\u63a8\u5bfc\u6b63\u5207\u51fd\u6570\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-tangente-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \u7684\u6b63\u5207\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f238988096540344626a3079f65a0753_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u8ba1\u7b97\u6b63\u5207\u7684\u5bfc\u6570\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u6211\u4eec\u4e0a\u9762\u770b\u5230\u7684\u4e09\u4e2a\u516c\u5f0f\u4e4b\u4e00\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u4f59\u5f26\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-47c1f81edd8b591f33ab986d4de73a34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u51fd\u6570 2x \u662f\u7ebf\u6027\u7684\uff0c\u56e0\u6b64\u5b83\u7684\u5bfc\u6570\u4e3a 2\u3002\u56e0\u6b64 2x \u7684\u6b63\u5207\u5bf9 2x \u4f59\u5f26\u5e73\u65b9\u7684\u5bfc\u6570\u4e3a 2\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-e18c22b2cabb93a6081363bc618840b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(2x)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{\\text{cos}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"405\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-tangente-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\u6b63\u5207\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c6defebe72239c5288ece20976d9a50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u6b63\u5207\u53c2\u6570\u51fd\u6570\u4e0d\u662f x\uff0c\u800c\u662f\u5177\u6709\u5bfc\u6570\u7684\u51fd\u6570\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u9700\u8981\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u63a8\u5bfc\u5b83\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-47c1f81edd8b591f33ab986d4de73a34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> x \u5e73\u65b9\u7684\u5bfc\u6570\u4e3a 2x\uff0c\u56e0\u6b64 x <sup>2<\/sup>\u7684\u6b63\u5207\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-111ca482f4c688c676c10b2ed80d6567_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{\\text{cos}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"403\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-tangente-al-cubo\"><\/span>\u793a\u4f8b 3\uff1a\u7acb\u65b9\u4f53\u5207\u7ebf\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a70568c32830f1f20ab7a5885bf999ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}^3(9x^2-4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"172\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u590d\u5408\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u8fd8\u9700\u8981\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u5fae\u5206\u5207\u7ebf\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-47c1f81edd8b591f33ab986d4de73a34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}(u)\\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{\\text{cos}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"387\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6b64\u5916\uff0c\u6b63\u5207\u662f 3 \u6b21\u65b9\uff0c\u8fd9\u610f\u5473\u7740\u5728\u5e94\u7528\u6b63\u5207\u5bfc\u6570\u516c\u5f0f\u4e4b\u524d\u5fc5\u987b\u4f7f\u7528\u5e42\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-424a7372a1d97a5c17a86d6253666164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=3\\text{tan}^2(9x^2-4x)\\cdot \\cfrac{18x-4}{\\text{cos}^2(9x^2-4x)} \\\\[2ex]&amp;=\\cfrac{3\\text{tan}^2(9x^2-4x)\\cdot(18x-4)}{\\text{cos}^2(9x^2-4x)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"110\" width=\"314\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-de-la-tangente-inversa\"><\/span>\u53cd\u6b63\u5207\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0e\u4efb\u4f55\u53cd\u51fd\u6570\u4e00\u6837\uff0c\u6b63\u5207\u51fd\u6570\u4e5f\u6709\u4e00\u4e2a\u53cd\u51fd\u6570\uff0c\u5373\u53cd\u6b63\u5207\u51fd\u6570\u3002\u5c3d\u7ba1\u5bfc\u51fa\u5b83\u7684\u516c\u5f0f\u4e0e\u6b63\u5207\u516c\u5f0f\u5e76\u4e0d\u76f8\u4f3c\uff0c\u4f46\u6211\u4eec\u5411\u60a8\u5c55\u793a\u5b83\u662f\u56e0\u4e3a\u5b83\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u5f88\u6709\u7528\u3002<\/p>\n<p>\u51fd\u6570<strong>\u53cd\u6b63\u5207\u7684\u5bfc\u6570<\/strong>\u662f\u51fd\u6570\u7684\u5bfc\u6570\u9664\u4ee5\u4e00\u52a0\u4e0a\u8be5\u51fd\u6570\u7684\u5e73\u65b9\u6240\u5f97\u7684\u5546<\/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-d26f5f19ebcdab218e6d1924e18845f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}^{-1}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"398\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c3x \u7684\u53cd\u6b63\u5207\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-bdabf1792179bdd9281695a65dcd0912_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{tan}^{-1}(3x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{3}{1+(3x)^2}=\\cfrac{3}{1+9x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"513\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-de-la-tangente\"><\/span>\u89e3\u51b3\u4e86\u5207\u7ebf\u5bfc\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u6b63\u5207\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-e0c187638a259878b3cf6382751c2718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{tan}(3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" 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-573c097d9cddb7837803e4aceaec362a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\text{tan}(x^3-10x^2+8)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" 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-4e140710c7f1fea51f3fe280f30fdb1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f(x)=\\text{tan}^2\\left(\\frac{x}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"153\" 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-49b86302e59ffb338f425f4e5a97be89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{tan}\\left(e^{2x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"151\" style=\"vertical-align: -7px;\"><\/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-4af042cb47d433a0eeff44d9c5349873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\text{tan}\\bigl(\\ln(4x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"171\" style=\"vertical-align: -7px;\"><\/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-21464f892729c58a42f796e0d35f6a89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{tan}\\left(\\sqrt{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"159\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-240652ca6b9fbabd52d65974bf3e4793_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{3}{\\text{cos}^2(3x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"156\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5166bb8a8d3af33cc82165b63e2b6a52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{3x^2-20x}{\\text{cos}^2(x^3-10x^2+8)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"241\" 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-94a4f0132583e89119dae1b25be65adf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f'(x)=2\\text{tan}\\left(\\frac{x}{2}\\right)\\cdot \\frac{1}{\\text{cos}^2\\left(\\frac{x}{2}\\right)}\\cdot \\frac{1}{2}=\\frac{\\text{tan}\\left(\\frac{x}{2}\\right)}{\\text{cos}^2\\left(\\frac{x}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"354\" 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-2d4f13da08be6a975b3e8710f5aee58c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=\\cfrac{2e^{2x}}{\\text{cos}^2(e^{2x})}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"160\" 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-cd7569c56712ac42fa2fe9300d9e4896_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{\\frac{4}{4x}}{\\text{cos}^2\\bigl(\\ln(4x)\\bigr)}=\\cfrac{1}{x\\cdot\\text{cos}^2\\bigl(\\ln(4x)\\bigr)}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"329\" 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-9a51deebd15244b70a6917a9ea2a456a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{\\frac{3}{2\\sqrt{3x}}}{\\text{cos}^2\\left(\\sqrt{3x}\\right)}=\\cfrac{3}{2\\sqrt{3x}\\cdot \\text{cos}^2\\left(\\sqrt{3x}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -21px;\"><\/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-la-tangente\"><\/span>\u6b63\u5207\u5bfc\u6570\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e0d\u662f\u4e00\u4e2a\u865a\u6784\u7684\u8868\u8fbe\u5f0f\uff0c\u5728\u672c\u8282\u4e2d\u6211\u4eec\u5c06\u4f7f\u7528\u6b63\u5207\u7684\u6570\u5b66\u5b9a\u4e49\u6765\u6f14\u793a\u6b63\u5207\u5bfc\u6570\u7684\u516c\u5f0f\u3002<\/p>\n<p>\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4ece\u8fde\u63a5\u4e09\u4e2a\u4e09\u89d2\u6bd4\u7387\u7684\u4e09\u89d2\u6052\u7b49\u5f0f\u5f00\u59cb\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-dbf6d65fa67f0a2161bd99ee7431f015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"124\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u6211\u4eec\u4f7f\u7528<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u9664\u5546\u7684\u5bfc\u6570\/\">\u9664\u6cd5\u7684\u5bfc\u6570\u516c\u5f0f<\/a><\/span>\uff0c\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-334dc33e2ef413b8d99dd7de50cebc74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\left(\\text{tan}(x)\\right)'=\\left(\\frac{\\text{sen}(x)}{\\text{cos}(x)}\\right)'\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"173\" 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-2b05dcbadd57bacdab9a7d4eda718e3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}(x)\\cdot \\text{cos}(x)+\\text{sen}(x)\\text{sen}(x) }{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"308\" 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-cf6fae22356a5ba2fe4f327843c0da81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}^2(x)+\\text{sen}^2(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"214\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4f46\u662f\uff0c\u4f7f\u7528\u57fa\u672c\u4e09\u89d2\u6052\u7b49\u5f0f\uff0c\u6211\u4eec\u77e5\u9053\u6b63\u5f26\u7684\u5e73\u65b9\u52a0\u4e0a\u4f59\u5f26\u7684\u5e73\u65b9\u662f 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-92d80771f891319379b2e756c5524aaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(x)+\\text{cos}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" 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-c737664b7a2ec3456d700d4939c15806_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{1}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"136\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u7b2c\u4e00\u4e2a\u6b63\u5207\u5bfc\u6570\u516c\u5f0f\u3002\u800c\u4e14\uff0c\u6b63\u5272\u662f\u4f59\u5f26\u7684\u4e58\u6cd5\u9006\u5143\uff0c\u56e0\u6b64\u4e5f\u63a8\u5bfc\u51fa\u7b2c\u4e8c\u4e2a\u8868\u8fbe\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-41f558939bb7b23e97112acb0630c4bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\text{sec}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"131\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6b63\u5207\u5bfc\u6570\u7684\u7b2c\u4e09\u6761\u89c4\u5219\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e0a\u4e00\u6b65\u7684\u5206\u6570\u8f6c\u5316\u4e3a\u5206\u6570\u548c\u6765\u8bc1\u660e\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-cf6fae22356a5ba2fe4f327843c0da81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}^2(x)+\\text{sen}^2(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"214\" 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-187bc0e3bc1c35a7dfd18197b94aa845_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=\\cfrac{\\text{cos}^2(x)}{\\text{cos}^2(x)}+\\cfrac{\\text{sen}^2(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"216\" 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-257a8cde825ce1b73cf5849d6a387507_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tan}'(x)=1+\\text{tan}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u6b63\u5207\u51fd\u6570\u662f\u5982\u4f55\u5bfc\u51fa\u7684\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5207\u7ebf\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u751a\u81f3\u53ef\u4ee5\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6700\u540e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%88%87%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u5207\u7ebf\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-31","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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