{"id":40,"date":"2023-09-17T10:58:44","date_gmt":"2023-09-17T10:58:44","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%89%b2%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0\/"},"modified":"2023-09-17T10:58:44","modified_gmt":"2023-09-17T10:58:44","slug":"%e5%89%b2%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%89%b2%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0\/","title":{"rendered":"\u6b63\u5272\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u6b63\u5272\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u9010\u6b65\u89e3\u51b3\u5272\u7ebf\u5bfc\u6570\u7684\u51e0\u4e2a\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u60a8\u5c06\u627e\u5230\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u516c\u5f0f\u6f14\u793a\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-de-la-secante\"><\/span>\u5272\u7ebf\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>x \u5272\u7ebf\u7684\u5bfc\u6570\u7b49\u4e8e x \u5272\u7ebf\u4e0e x \u6b63\u5207\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-96448e16137a4b0d5cda8192ec339ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(x)\\cdot \\text{tan}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"434\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u901a\u8fc7\u5e94\u7528\u4e09\u89d2\u516c\u5f0f\uff0cx \u7684\u6b63\u5272\u5bfc\u6570\u4e5f\u53ef\u4ee5\u5b9a\u4e49\u4e3a x \u7684\u6b63\u5f26\u9664\u4ee5 x \u7684\u4f59\u5f26\u5e73\u65b9\u7684\u5546\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-7055796dc0e57b6284a41ca70ecca764_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{sec}(x)\\cdot \\text{tan}(x)=\\cfrac{1}{\\text{cos}(x)}\\cdot \\cfrac{\\text{sen}(x)}{\\text{cos}(x)}=\\cfrac{\\text{sen}(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"390\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u6211\u4eec\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\uff0c<strong>\u51fd\u6570\u6b63\u5272\u7684\u5bfc\u6570<\/strong>\u5c31\u662f\u51fd\u6570\u7684\u6b63\u5272\u4e58\u4ee5\u51fd\u6570\u7684\u6b63\u5207\u518d\u4e58\u4ee5\u51fd\u6570\u7684\u5bfc\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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u6b63\u5272\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\u5982\u4e0b\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\/derive-de-la-secante.webp\" alt=\"\u7531\u5272\u7ebf\u5bfc\u51fa\" class=\"wp-image-2351\" width=\"475\" height=\"314\" 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-secante\"><\/span>\u6b63\u5272\u5bfc\u6570\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u6b63\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u5c06\u89e3\u51b3\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u51e0\u4e2a\u4f8b\u5b50\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-secante-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \u6b63\u5272\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5c06\u770b\u5230 2x \u5272\u7ebf\u7684\u5bfc\u6570\u503c\u591a\u5c11\u94b1\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-c8a3b19bc9ee15896b5416920d623745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"113\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u5bfc\u51fa 2x \u51fd\u6570\u7684\u6b63\u5272\uff0c\u5fc5\u987b\u4f7f\u7528\u5176\u76f8\u5e94\u7684\u516c\u5f0f\u3002\u53e6\u5916\uff0c\u5728\u6b63\u5272\u53c2\u6570\u4e2d\uff0c\u6211\u4eec\u6709 x \u4ee5\u5916\u7684\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5e94\u7528\u94fe\u5f0f\u6cd5\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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u51fd\u6570 2x \u662f\u7ebf\u6027\u7684\uff0c\u56e0\u6b64\u5b83\u7684\u5bfc\u6570\u4e3a 2\u3002\u56e0\u6b64\uff0c\u8981\u6c42\u5bfc\u6570\uff0c\u6211\u4eec\u53ea\u9700\u5c06\u516c\u5f0f\u4e2d\u7684 u \u66ff\u6362\u4e3a 2x\uff0c\u5c06 u&#8217; \u66ff\u6362\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-2decb8aff43ac88c25cae4f6c1443b70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(2x)\\cdot \\text{tan}(2x)\\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"482\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-secante-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\u6b63\u5272\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u672c\u7ec3\u4e60\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3 x \u5e73\u65b9\u6b63\u5272\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\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-e1359b6d31f1ec6172c29ec2066b3fb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8981\u5bfc\u51fa\u51fd\u6570\u7684\u6b63\u5272\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u770b\u5230\u7684\u4e24\u4e2a\u516c\u5f0f\u4e4b\u4e00\uff0c\u4f46\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u6b63\u5272\u548c\u6b63\u5207\u4e4b\u95f4\u7684\u4e58\u6cd5\u516c\u5f0f\u5bf9\u51fd\u6570\u8fdb\u884c\u5fae\u5206\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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> x \u7684 2 \u6b21\u65b9\u5bfc\u6570\u4e3a 2x\uff0c\u56e0\u6b64 x \u5e73\u65b9\u6b63\u5272\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-2e0bdd83c01111c51620bd6a558a5930_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(x^2)\\cdot \\text{tan}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"490\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-secante-al-cubo-de-un-polinomio\"><\/span>\u793a\u4f8b 3\uff1a\u591a\u9879\u5f0f\u6b63\u5272\u7acb\u65b9\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-6ee68247e5fd1854b875d655b1615701_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}^3(x^5+4x^2-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u51fd\u6570\u6b63\u5272\u7684\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-0ac73f3fef391bac629871e7035160d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\text{sec}(u)\\cdot \\text{tan}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"462\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f46\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5fc5\u987b\u5bfc\u51fa\u4e00\u4e2a\u590d\u5408\u51fd\u6570\uff0c\u56e0\u4e3a\u6b63\u5272\u88ab\u63d0\u5347\u5230\u4e09\u6b21\u65b9\uff0c\u800c\u4e14\uff0c\u5728\u5b83\u7684\u53c2\u6570\u4e2d\u6211\u4eec\u6709\u4e00\u4e2a\u591a\u9879\u5f0f\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u5bf9\u6574\u4e2a\u51fd\u6570\u6c42\u5bfc\uff0c\u6211\u4eec\u9700\u8981\u5e94\u7528\u94fe\u5f0f\u6cd5\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-7ab88cc23ab3fb559e2386cd52637082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp; =3\\text{sec}^2(x^5+4x^2-3)\\text{sec}(x^5+4x^2-3)\\text{tan}(x^5+4x^2-3)(5x^4+8x)\\\\[1.5ex]&amp;=3\\text{sec}^3(x^5+4x^2-3)\\text{tan}(x^5+4x^2-3)(5x^4+8x)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"562\" 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-una-secante\"><\/span>\u89e3\u51b3\u4e86\u5272\u7ebf\u5bfc\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a8\u5bfc\u4ee5\u4e0b\u6b63\u5272\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-a63efa4ccc6266dc6db9552b5663ccb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sec}(x^6-6x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"186\" 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-d4cd03385df118ead733c64d1524bb36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{sec}^4(5x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" 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-6b8e0ec036c5a0ccaca77d1116a2606a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{sec}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"159\" 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-787d864c315ebf629c2505df13cfdf70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sec}\\left(e^{x^2+3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"178\" style=\"vertical-align: -11px;\"><\/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-1e9e9e0065335901bb018afd8458bf7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sec}\\left(\\sqrt{5x+1}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"187\" 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-c162c3a202d8d10ed26b6f5ad4afe7f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{sec}(x^6-6x^3)\\cdot \\text{tan}(x^6-6x^3)\\cdot (6x^5-18x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"415\" 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-72985d8bce95d808b9070bc7b834b271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{B) }f(x)&amp; =4\\text{sec}^3(5x^4)\\cdot \\text{sec}(5x^4)\\cdot \\text{tan}(5x^4)\\cdot 20x^3\\\\[1.5ex] &amp;=4\\text{sec}^4(5x^4)\\cdot \\text{tan}(5x^4)\\cdot 20x^3\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"366\" 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-1a89fb7e8b228b31af9979a4fc0b08ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{sec}\\bigl(\\ln(x)\\bigr)\\cdot \\text{tan}\\bigl(\\ln(x)\\bigr)\\cdot \\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"281\" 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-7a488bce8bdd2cb66ebb028ca017f172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{sec}\\left(e^{x^2+3x}\\right)\\cdot \\text{tan}\\left(e^{x^2+3x}\\right)\\cdot e^{x^2+3x}\\cdot (2x+3)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"429\" style=\"vertical-align: -11px;\"><\/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-b1bb860fafc464f3c8a30bf3e9b29a94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{sec}\\left(\\sqrt{5x+1}\\right)\\cdot \\text{tan}\\left(\\sqrt{5x+1}\\right)\\cdot \\cfrac{5}{2\\sqrt{5x+1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"400\" style=\"vertical-align: -16px;\"><\/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-formula-de-la-derivada-de-la-secante\"><\/span>\u6b63\u5272\u5bfc\u6570\u516c\u5f0f\u7684\u6f14\u793a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u8bc1\u660e\u6b63\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u867d\u7136\u663e\u7136\u6ca1\u6709\u5fc5\u8981\u719f\u8bb0\u8bc1\u660e\uff0c\u4f46\u4e86\u89e3\u516c\u5f0f\u7684\u6765\u6e90\u603b\u662f\u6709\u597d\u5904\u7684\u3002<\/p>\n<p>\u4ece\u6570\u5b66\u4e0a\u6765\u8bf4\uff0c\u6b63\u5272\u7684\u5b9a\u4e49\u662f\u4f59\u5f26\u7684\u4e58\u6cd5\u9006\u5143\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-8e3493c8e50b7c4b713b7c0f6ea9eca9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sec}(x)=\\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"178\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5c1d\u8bd5\u4f7f\u7528\u5546\u89c4\u5219\u5bfc\u51fa\u6b63\u5272\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-37c02387c22125a313ff7fe65c1a7b37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"121\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5e76\u4e14\uff0c\u6b63\u5982\u6211\u4eec\u5728\u7b2c\u4e00\u90e8\u5206\u4e2d\u770b\u5230\u7684\uff0c\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u53ef\u4ee5\u8f6c\u6362\u4e3a\u6b63\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u5206\u6570\u5206\u6210\u4e24\u4e2a\u4e0d\u540c\u7684\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-eb2f40cc564d430340271ea1b7659084_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{\\text{sen}(x)}{\\text{cos}(x)}\\cdot \\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6b63\u5f26\u9664\u4ee5\u4f59\u5f26\u7b49\u4e8e\u6b63\u5207\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u6240\u8ff0\u5546\u66ff\u6362\u4e3a\u6b63\u5207\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-3ce86a0b57ad6e2322c169eb90d9e8bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{tan}(x)\\cdot \\cfrac{1}{\\text{cos}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"175\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6839\u636e\u6b63\u5272\u51fd\u6570\u7684\u6570\u5b66\u5b9a\u4e49\uff0c\u4f59\u5f26\u662f\u5176\u9006\u4e58\u6cd5\u3002\u56e0\u6b64\uff0c\u901a\u8fc7\u5c06 1 \u9664\u4ee5\u4f59\u5f26\u9664\u4ee5\u5272\u7ebf\uff0c\u6211\u4eec\u5f97\u51fa\u5176\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-d0ea3bb9b42cd0a3474363910fee95bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{tan}(x)\\cdot \\text{sec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u6b63\u5272\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u9010\u6b65\u89e3\u51b3\u5272\u7ebf\u5bfc\u6570\u7684\u51e0\u4e2a\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u60a8\u5c06\u627e\u5230\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u516c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%89%b2%e7%ba%bf%e7%9a%84%e5%af%bc%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u6b63\u5272\u7684\u5bfc\u6570<\/span> \u67e5\u770b\u5168\u6587 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