{"id":374,"date":"2023-07-03T16:46:24","date_gmt":"2023-07-03T16:46:24","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%8b%89%e8%80%83%e8%be%9b%e8%a1%8d%e7%94%9f%e7%89%a9\/"},"modified":"2023-07-03T16:46:24","modified_gmt":"2023-07-03T16:46:24","slug":"%e6%8b%89%e8%80%83%e8%be%9b%e8%a1%8d%e7%94%9f%e7%89%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%8b%89%e8%80%83%e8%be%9b%e8%a1%8d%e7%94%9f%e7%89%a9\/","title":{"rendered":"\u53cd\u4f59\u5f26\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cd\u4f59\u5f26\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u4f1a\u627e\u5230\u53cd\u4f59\u5f26\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u5e76\u4e14\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u6211\u4eec\u5411\u60a8\u5c55\u793a\u53cd\u4f59\u5f26\u5bfc\u6570\u516c\u5f0f\u7684\u8bc1\u660e\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcocoseno\"><\/span>\u53cd\u4f59\u5f26\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>x \u7684\u53cd\u4f59\u5f26\u5bfc\u6570\u662f 1 \u51cf\u53bb x \u5e73\u65b9\u7684\u5e73\u65b9\u6839\u7684\u8d1f\u4e00\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-08ccbc72f9a1b83be4c2d4ce41e7f10e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u51fd\u6570\u53cd\u4f59\u5f26\u7684\u5bfc\u6570<\/strong>\u7b49\u4e8e\u51cf\u53bb\u8be5\u51fd\u6570\u7684\u5bfc\u6570\u9664\u4ee5\u4e00\u7684\u5e73\u65b9\u6839\u51cf\u53bb\u8be5\u51fd\u6570\u7684\u5e73\u65b9\u6240\u5f97\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u7b2c\u4e00\u4e2a\u516c\u5f0f\u5c31\u662f\u7528u\u4ee3\u66ff\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4e2d\u7684x\u5f97\u5230\u7684\u3002\u56e0\u6b64\uff0c\u56de\u987e\u4e00\u4e0b\uff0c\u53cd\u4f59\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\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\/derive-arc-cosinus.webp\" alt=\"\u53cd\u4f59\u5f26\u5bfc\u6570\" class=\"wp-image-1973\" width=\"432\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5982\u60a8\u6240\u89c1\uff0c\u53cd\u4f59\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\u7c7b\u4f3c\u4e8e<span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u62c9\u514b\u8f9b\u884d\u751f\u7269\/\">\u53cd\u6b63\u5f26\u5bfc\u6570<\/a><\/span>\uff0c\u4f46\u5728\u5176\u524d\u9762\u6dfb\u52a0\u4e86\u4e00\u4e2a\u8d1f\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcocoseno\"><\/span>\u53cd\u4f59\u5f26\u5bfc\u6570\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u53cd\u4f59\u5f26\u51fd\u6570\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u73b0\u5728\u5c06\u5206\u6790\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u51e0\u4e2a\u793a\u4f8b\u3002\u8fd9\u6837\u60a8\u4f1a\u66f4\u5bb9\u6613\u7406\u89e3\u51fd\u6570\u7684\u53cd\u4f59\u5f26\u662f\u5982\u4f55\u5bfc\u51fa\u7684\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcocoseno-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \u7684\u53cd\u4f59\u5f26\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-c913be328da0f829a3545ccf101e15e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e3a\u4e86\u6c42\u89e3\u53cd\u4f59\u5f26\u7684\u5bfc\u6570\uff0c\u6211\u4eec\u4f7f\u7528\u5b83\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> 2x \u7684\u5bfc\u6570\u662f 2\uff0c\u56e0\u6b64 2x \u7684\u53cd\u4f59\u5f26\u5bfc\u6570\u662f\u6839 1 \u51cf\u53bb 2x \u5e73\u65b9\u7684\u8d1f 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-cf892a94fcba0edb3ae5c4d8ff013899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2}{\\sqrt{1-(2x)^2}}=-\\cfrac{2}{\\sqrt{1-4x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"576\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcocoseno-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\u7684\u53cd\u4f59\u5f26\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-b2f6ac6474aa61a7eddba4bb79a45ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u5e94\u7528\u53cd\u4f59\u5f26\u5bfc\u6570\u516c\u5f0f\u548c\u94fe\u5f0f\u6cd5\u5219\u6765\u8ba1\u7b97\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e\u51fd\u6570 x <sup>2<\/sup>\u7684\u5bfc\u6570\u4e3a 2x\uff0c\u56e0\u6b64 x \u7684\u53cd\u4f59\u5f26\u5bf9 2 \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-e9180f04fd27262ca57f4b648c3b6b9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x}{\\sqrt{1-\\left(x^2\\right)^2}}=-\\cfrac{2x}{\\sqrt{1-x^4}}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"565\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcocoseno-de-un-logaritmo\"><\/span>\u793a\u4f8b 3\uff1a\u5bf9\u6570\u53cd\u4f59\u5f26\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-d172240febea273fb3978225f13eebad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u672c\u4f8b\u4e2d\u7684\u51fd\u6570\u662f\u4e00\u4e2a\u7531\u53cd\u4f59\u5f26\u548c\u81ea\u7136\u5bf9\u6570\u7ec4\u6210\u7684\u51fd\u6570\uff0c\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4f7f\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-e38d63c25970ce1d6d71ff542b26ce89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'}{\\sqrt{1-u^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"430\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u81ea\u7136\u5bf9\u6570\u7684\u5bfc\u6570\u662f\u4e00\u9664\u4ee5 x\uff0c\u56e0\u6b64\u6574\u6570\u51fd\u6570\u7684\u5bfc\u6570\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-d682371fc7d064383f30416a40a4f9ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arccos}\\bigl(\\ln (x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\cfrac{1}{x}}{\\sqrt{1-\\left(\\ln(x)\\right)^2}}=\\cfrac{1}{x\\sqrt{1-\\ln^2(x)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"582\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcocoseno\"><\/span>\u53cd\u4f59\u5f26\u5bfc\u6570\u89e3\u51b3\u4e86\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a8\u5bfc\u4ee5\u4e0b\u53cd\u4f59\u5f26\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-35e2715201a91cea5d5a914619695b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{arccos}(7x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" 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-a2bc15a65a4f4e6c42effc3e21437657_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{arccos}(x^3+6x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" 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-38ed3b9ec0b9a3cb6443dec0c6afb6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{arccos}^3\\left(e^{3x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" 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-766af35119810145dd3589fab05d2f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arccos}\\left(\\log_3(x^3)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" 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-ce6b5d78ea798a70c51759cce27e5b25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arccos}\\left(\\sqrt{4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"181\" 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-79dbfad4db01cc46534b4875a7a8c905_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f'(x)=-\\cfrac{7}{\\sqrt{1-(7x)^2}}=-\\cfrac{7}{\\sqrt{1-49x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"314\" 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-fd07daef79650fcb34116e266aee09fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=-\\cfrac{3x^2+6}{\\sqrt{1-(x^3+6x)^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"233\" 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-0ffd255c55afc3967dc250bc63741575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }\\displaystyle f'(x)&amp;=3\\text{arccos}^2\\left(e^{3x}\\right)\\cdot \\left(-\\frac{3e^{3x}}{\\sqrt{1-\\left(e^{3x}\\right)^2}}\\right)\\\\[1.5ex] &amp;=-\\cfrac{9\\text{arccos}^2\\left(e^{3x}\\right)\\cdot e^{3x}}{\\sqrt{1-e^{6x}}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"131\" width=\"346\" 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-ec25311613f0552bbc52d2d15581d3fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp;=-\\cfrac{1}{\\sqrt{1-\\left(\\log_3(3x)\\right)^2}}\\cdot \\cfrac{3}{3x\\cdot \\ln 3}\\\\[1.5ex] &amp;=-\\cfrac{1}{x\\cdot \\ln 3\\cdot \\sqrt{1-\\log_3^2(3x)}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"133\" width=\"312\" 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-d1a362c38a56084dec3c6ebbccba9ab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) } f'(x)&amp; =-\\cfrac{1}{\\sqrt{1-\\left(\\sqrt{4x}\\right)^2}}\\cdot \\cfrac{4}{2\\sqrt{4x}}\\\\[1.5ex] &amp;=-\\cfrac{2}{\\sqrt{1-4x}\\cdot 2\\sqrt{x}}\\\\[1.5ex] &amp;=-\\cfrac{1}{\\sqrt{x-4x^2}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"184\" width=\"267\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"demostracion-de-la-formula-de-la-derivada-del-arcocoseno\"><\/span>\u53cd\u4f59\u5f26\u5bfc\u6570\u516c\u5f0f\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u6f14\u793a\u53cd\u4f59\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\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-0a3001135fdded9698f51b8a683036c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arccos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u5c06\u53cd\u4f59\u5f26\u8f6c\u6362\u4e3a\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-32b94bb993d1256aa9088d9bffbb0941_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{cos}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u63a8\u5bfc\u51fa\u7b49\u5f0f\u7684\u4e24\u8fb9\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-e5f229f3e26b190eca429017bd78dba0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=-\\text{sen}(y)\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u6e05\u9664\u4f60\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-b2c2f95f5c7999d81cd10976320a7413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\text{sen}(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u4f7f\u7528\u57fa\u672c\u7684\u4e09\u89d2\u6052\u7b49\u5f0f\u5c06\u6b63\u5f26\u53d8\u4e3a\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-9af2ef5387e227b363035275ba0777e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1 \\ \\longrightarrow \\ \\text{sen}(y)=\\sqrt{1-\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"390\" style=\"vertical-align: -6px;\"><\/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-3c3807ba3700aac7694b04356a9a25d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"157\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p>\u4f46\u4e0a\u9762\u6211\u4eec\u63a8\u5bfc\u51fa x \u7b49\u4e8e y \u7684\u4f59\u5f26\uff0c\u6240\u4ee5\u65b9\u7a0b\u4ecd\u7136\u6210\u7acb\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-8c3b21ba43e58ec763ab27498aa4fb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=-\\cfrac{1}{\\sqrt{1-x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"117\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u53cd\u4f59\u5f26\u5bfc\u6570\u7684\u8868\u8fbe\u5f0f\uff0c\u56e0\u6b64\u8bc1\u660e\u4e86\u5b83\u7684\u516c\u5f0f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u91cc\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\u7684\u53cd\u4f59\u5f26\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u4f1a\u627e\u5230\u53cd\u4f59\u5f26\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u5e76\u4e14\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6700 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%8b%89%e8%80%83%e8%be%9b%e8%a1%8d%e7%94%9f%e7%89%a9\/\"> <span class=\"screen-reader-text\">\u53cd\u4f59\u5f26\u7684\u5bfc\u6570<\/span> \u67e5\u770b\u5168\u6587 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