{"id":30,"date":"2023-09-17T11:02:59","date_gmt":"2023-09-17T11:02:59","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%94%b1%e4%bd%99%e5%bc%a6%e5%af%bc%e5%87%ba\/"},"modified":"2023-09-17T11:02:59","modified_gmt":"2023-09-17T11:02:59","slug":"%e7%94%b1%e4%bd%99%e5%bc%a6%e5%af%bc%e5%87%ba","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%94%b1%e4%bd%99%e5%bc%a6%e5%af%bc%e5%87%ba\/","title":{"rendered":"\u4f59\u5f26\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u4f59\u5f26\u51fd\u6570\uff08\u516c\u5f0f\uff09\u3002\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4f59\u5f26\u51fd\u6570\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u5e76\u901a\u8fc7\u9010\u6b65\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5411\u60a8\u5c55\u793a\u4e86\u516c\u5f0f\u7684\u8bc1\u660e\uff0c\u4ec0\u4e48\u662f\u4f59\u5f26\u7684\u4e8c\u9636\u5bfc\u6570\uff0c\u751a\u81f3\u662f\u53cd\u4f59\u5f26\u7684\u5bfc\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-coseno\"><\/span>\u4f59\u5f26\u7684\u5bfc\u6570\u662f\u4ec0\u4e48\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4f59\u5f26\u51fd\u6570\u7684\u5bfc\u6570\u662f\u7b26\u53f7\u4fee\u6b63\u7684\u6b63\u5f26\u51fd\u6570\u3002\u6362\u53e5\u8bdd\u8bf4\uff0cx\u7684\u4f59\u5f26\u5bfc\u6570\u7b49\u4e8e\u51cf\u53bbx\u7684\u6b63\u5f26\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-72551067d650b8d3797bc37497ec609d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"389\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u4f59\u5f26\u53c2\u6570\u4e2d\u6709\u4e00\u4e2a\u51fd\u6570\uff0c\u5219\u4f59\u5f26\u7684\u5bfc\u6570\u662f\u51cf\u53bb\u8be5\u51fd\u6570\u7684\u6b63\u5f26\u503c\u4e58\u4ee5\u8be5\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-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7b2c\u4e8c\u4e2a\u516c\u5f0f\u4e0e\u7b2c\u4e00\u4e2a\u516c\u5f0f\u7b49\u6548\uff0c\u4f46\u5e94\u7528\u4e86\u94fe\u5f0f\u6cd5\u5219\u3002\u6240\u4ee5\uff0c\u7efc\u4e0a\u6240\u8ff0\uff0c\u4f59\u5f26\u5bfc\u6570\u7684\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\/derivee-du-cosinus.webp\" alt=\"\u4f59\u5f26\u5bfc\u6570\" class=\"wp-image-1902\" width=\"428\" height=\"292\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-coseno\"><\/span>\u4f59\u5f26\u5bfc\u6570\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u4f59\u5f26\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u6b64\u7c7b\u4e09\u89d2\u5bfc\u6570\u7684\u51e0\u4e2a\u4f8b\u5b50\uff0c\u4ee5\u4fbf\u60a8\u5bf9\u5982\u4f55\u63a8\u5bfc\u4f59\u5f26\u51fd\u6570\u4e0d\u518d\u6709\u7591\u95ee\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-coseno-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \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-87c696135df266b2d8498b353bf03c36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u4f59\u5f26\u53c2\u6570\u4e2d\uff0c\u6211\u4eec\u6ca1\u6709\u5355\u4e2a x\uff0c\u800c\u662f\u4e00\u4e2a\u66f4\u590d\u6742\u7684\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u4e0b\u9762\u7684\u516c\u5f0f\u6765\u63a8\u5bfc\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-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7531\u4e8e 2x \u7684\u5bfc\u6570\u4e3a 2\uff0c\u56e0\u6b64 2x \u7684\u4f59\u5f26\u5bfc\u6570\u5c06\u51cf\u53bb 2x \u7684\u6b63\u5f26\u4e58\u4ee5 2\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-ba75c906f1694fe3fbd16fa61e0d288e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(2x)\\cdot 2=-2\\text{sen}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"532\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-coseno-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\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-89f1a1fc3f2d5e95aafbd2a37282f88c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"113\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e0e\u524d\u9762\u7684\u793a\u4f8b\u4e00\u6837\uff0c\u5728\u4f59\u5f26\u53c2\u6570\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u4e0e x \u4e0d\u540c\u7684\u51fd\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\u6765\u5bfc\u51fa\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-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u90a3\u4e48\uff0cx <sup>2<\/sup>\u7684\u5bfc\u6570\u4e3a 2x\uff0c\u56e0\u6b64\uff0cx \u7684\u4f59\u5f26\u7684 2 \u6b21\u65b9\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-a410f3316194c86b97a987b0ec7e9e6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(x^2)\\cdot 2x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"437\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-coseno-al-cubo\"><\/span>\u793a\u4f8b 3\uff1a\u4f59\u5f26\u4e09\u6b21\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-dfa2e76d23ef3aeb2ab3ff8e20e2aa07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}^3(2x^6-5x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"178\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u672c\u4f8b\u4e2d\u7684\u4f59\u5f26\u51fd\u6570\u662f\u7531\u53e6\u4e00\u4e2a\u51fd\u6570\u7ec4\u6210\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u6765\u6c42\u89e3\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-ccc4f6fce30c027f8782a296a44b84b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\text{sen}(u)\\cdot u'\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"416\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u901a\u8fc7\u5e94\u7528\u516c\u5f0f\uff0c\u6211\u4eec\u5f97\u5230\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-73284bcfb1d5647b2304e323e7fbaedf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=3\\text{cos}^2(2x^6-5x^3)\\cdot \\bigl(-\\text{sen}(2x^6-5x^3)\\bigr)\\cdot (12x^5-15x^2)\\\\[2ex]&amp;=-3\\text{cos}^2(2x^6-5x^3)\\cdot \\text{sen}(2x^6-5x^3)\\cdot (12x^5-15x^2)\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"467\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><u style=\"text-decoration-color:#ff951b;\">\u4e3a\u4e86\u5bf9\u8be5\u51fd\u6570\u6c42\u5bfc\uff0c\u8fd8\u5fc5\u987b\u4f7f\u7528<\/u><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u529f\u7387\u52bf\u51fd\u6570\u7684\u5bfc\u6570\/\">\u52bf\u51fd\u6570\u7684\u5bfc<\/a><\/span>\u6570\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"segunda-derivada-del-coseno\"><\/span>\u4f59\u5f26\u7684\u4e8c\u9636\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u770b\u5230\uff0c\u7531\u4e8e\u4e09\u89d2\u51fd\u6570\u7684\u7279\u6027\uff0c\u6b63\u5f26\u7684\u4e8c\u9636\u5bfc\u6570\u53ef\u4ee5\u5f88\u5bb9\u6613\u8ba1\u7b97\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><u style=\"text-decoration-color:#ff951b;\"><strong>\u6ce8\u610f\uff1a<\/strong>\u8981\u7406\u89e3\u4e0b\u9762\u7684\u5185\u5bb9\uff0c\u4f60\u9700\u8981\u77e5\u9053<\/u><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6b63\u5f26\u5bfc\u6570\/\">\u4ec0\u4e48\u662f\u6b63\u5f26\u7684\u5bfc\u6570<\/a><\/span>\u3002<\/p>\n<p> <strong>x \u7684\u4f59\u5f26\u4e8c\u9636\u5bfc\u6570\u51cf\u53bb x \u7684\u4f59\u5f26\u3002<\/strong>\u8fd9\u53ef\u80fd\u770b\u8d77\u6765\u5f88\u5947\u602a\uff0c\u4f46\u4ece\u6570\u5b66\u4e0a\u6765\u8bf4\u786e\u5b9e\u5982\u6b64\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6b63\u5f26\u7684\u5bfc\u6570\u662f\u4f59\u5f26\uff0c\u56e0\u6b64\uff0c\u901a\u8fc7\u5bf9 x \u7684\u4f59\u5f26\u6c42\u4e24\u6b21\u5fae\u5206\uff0c\u53ef\u4ee5\u518d\u6b21\u83b7\u5f97\u4f59\u5f26\uff0c\u4f46\u7b26\u53f7\u6709\u6240\u6539\u53d8\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-d0d9dda8a4031c367120b1f950da4391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cos}(x)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=-\\text{sen}(x)\\\\[2ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{cos}(x)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"157\" width=\"132\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u4f59\u5f26\u53c2\u6570\u4e0d\u662f x\uff0c\u5219\u6b64\u5c5e\u6027\u4f1a\u53d1\u751f\u53d8\u5316\uff0c\u56e0\u4e3a\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u62d6\u52a8\u94fe\u5f0f\u6cd5\u5219\u7684\u9879\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-83d86bd6508f06b0723153b3b9254c1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\text{cos}(u)\\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f'(x)=-\\text{sen}(u)\\cdot u' \\\\[1.5ex] \\quad\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex] f''(x)=-\\text{cos}(u)\\cdot u'^2 -\\text{sen}(u)\\cdot u'' \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"153\" width=\"263\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"derivada-del-coseno-inverso\"><\/span>\u53cd\u4f59\u5f26\u7684\u5bfc\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6240\u6709\u4e09\u89d2\u51fd\u6570\u90fd\u6709\u53cd\u51fd\u6570\uff0c\u56e0\u6b64\u4f59\u5f26\u51fd\u6570\u4e5f\u53ef\u4ee5\u53cd\u51fd\u6570\u3002\u540c\u6837\uff0c\u53cd\u4f59\u5f26\u662f\u53ef\u5fae\u7684\u3002<\/p>\n<p>\u51fd\u6570<strong>\u7684\u53cd\u4f59\u5f26\u5bfc\u6570<\/strong>\u51cf\u53bb\u8be5\u51fd\u6570\u7684\u5bfc\u6570\u9664\u4ee5\u4e00\u7684\u5e73\u65b9\u6839\u51cf\u53bb\u8be5\u51fd\u6570\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-307f91156ee9c404e9c1a1c0de56b102_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}^{-1}(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=\"425\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u53cd\u4f59\u5f26\u4e5f\u79f0\u4e3a\u53cd\u4f59\u5f26\u3002<\/p>\n<p>\u4f8b\u5982\uff0c3x \u7684\u53cd\u4f59\u5f26\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-7ce426dcd95d21e43b182ef593520c16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cos}^{-1}(3x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{3}{\\sqrt{1-(3x)^2}}=-\\cfrac{3}{\\sqrt{1-9x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"571\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-coseno\"><\/span>\u89e3\u51b3\u4e86\u4f59\u5f26\u5bfc\u6570\u7684\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8ba1\u7b97\u4ee5\u4e0b\u4f59\u5f26\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-c1caebbb3b9acfa8cd25721299f9a22e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{cos}(4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" 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-a89d6e415addae7423aa75362416686b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\text{cos}(2x^3-5x+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"218\" 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-dad34285ad7ac07f34ef408c65cbb96c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f(x)=9\\text{cos}\\left(\\frac{x}{3}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"152\" 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-752bff297c20cdf69d6fcb45290be935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{cos}^5(x^2+3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"187\" 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-939dee8bcafba3f55812c5a13f27a309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\text{cos}\\left(e^{5x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"148\" 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-f6c7c3c5786d010b99f4e65b692dfe1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } \\displaystyle f(x)=9\\text{cos}\\left(\\frac{e^x}{5x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"164\" 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-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a3e1b1b2fe486d1c432a075c0028b62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=-\\text{sen}(4x)\\cdot 4 =-4\\text{sen}(4x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"285\" 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-8bc2f2e1676bb5f0d4ca231bd35b2b12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=-\\text{sen}(2x^3-5x+1)\\cdot (6x^2-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"321\" 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-cc5cf86d30b34d4cd1a794a4d2ee6a5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } \\displaystyle f'(x)=-9\\text{sen}\\left(\\frac{x}{3}\\right)\\cdot \\frac{1}{3} =-3\\text{sen}\\left(\\frac{x}{3}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"306\" 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-f168f2e897b18c662f567a25ff09e881_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=-5\\text{cos}^4(x^2+3x)\\cdot \\text{sen}(x^2+3x)\\cdot (2x+3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"401\" 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-fe49736d7a1ce1736679e8c25bc4a66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=-\\text{sen}\\left(e^{5x}\\right)\\cdot e^{5x}\\cdot 5=-5\\text{sen}\\left(e^{5x}\\right)\\cdot e^{5x}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"377\" 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-9f4645fb77435daec6f696cffbd54884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{F) }\\displaystyle f'(x)&amp;=-9\\text{sen}\\left(\\frac{e^x}{5x}\\right)\\cdot \\frac{e^x\\cdot 5x-e^x\\cdot 5}{(5x)^2}\\\\[2ex]&amp;=-9\\text{sen}\\left(\\frac{e^x}{5x}\\right)\\cdot \\frac{5e^x(x-1)}{25x^2}\\\\[2ex]&amp;=-9\\text{sen}\\left(\\frac{e^x}{5x}\\right)\\cdot \\frac{e^x(x-1)}{5x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"172\" width=\"310\" 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-derivada-del-coseno\"><\/span>\u4f59\u5f26\u5bfc\u6570\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u4ee5\u6570\u5b66\u65b9\u5f0f\u6f14\u793a x \u4f59\u5f26\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u5bfc\u6570\u7684\u5b9a\u4e49\uff0c\u5b83\u5bf9\u5e94\u4e8e\u4ee5\u4e0b\u9650\u5236\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-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>\u6211\u4eec\u8981\u8bc1\u660e\u4f59\u5f26\uff0c\u6240\u4ee5\u51fd\u6570\u662f cos(x)\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-a00c11698e4b4f5caf0f227e18be8656_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{cos}(x+h)-\\text{cos}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"245\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u4e0d\u80fd\u901a\u8fc7\u66ff\u4ee3\u6765\u89e3\u51b3\u8fd9\u4e2a\u9650\u5236\uff0c\u56e0\u4e3a\u6211\u4eec\u6700\u7ec8\u4f1a\u9677\u5165\u4e0d\u786e\u5b9a\u6027\u3002\u4f46\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5e94\u7528\u4ee5\u4e0b\u4e09\u89d2\u6052\u7b49\u5f0f\u4ee5\u53e6\u4e00\u79cd\u65b9\u5f0f\u8868\u8fbe\u603b\u548c\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-5e06f1728cce31fb5650ba149b8e5b9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cos}(a+b)=\\text{cos}(a)\\text{cos}(b)-\\text{sen}(a)\\text{sen}(b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"307\" 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-db64449e24b11a613417ebce4c7c7a85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{cos}(x)\\text{cos}(h)-\\text{sen}(x)\\text{sen}(h)-\\text{cos}(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"380\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u4e0b\u4e00\u6b65\u662f\u5c06\u5206\u6570\u5206\u6210\u4e24\u4e2a\u5206\u6570\u5e76\u53d6\u4f59\u5f26\u7684\u516c\u56e0\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-c7c1cd89cf290b01d7d72fc8084f6529_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\left[\\frac{\\text{cos}(x)\\bigl(\\text{cos}(h)-1\\bigr)}{h}-\\frac{\\text{sen}(x)\\text{sen}(h)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"380\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u51cf\u6cd5\u7684\u6781\u9650\u7b49\u4e8e\u6781\u9650\u7684\u51cf\u6cd5\uff0c\u56e0\u6b64\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-739fc9a2280c7da1bf2ea830ee5ec88c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\text{cos}(x)\\bigl(\\text{cos}(h)-1\\bigr)}{h}-\\lim_{h \\to 0}\\frac{\\text{sen}(x)\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"393\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> x \u7684\u4f59\u5f26\u548c x \u7684\u6b63\u5f26\u4e0d\u4f9d\u8d56\u4e8e h\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u5c06\u5b83\u4eec\u63d0\u53d6\u5230\u754c\u9650\u4e4b\u5916\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-bfbc83e5a84d91a0f6d98418a4f0041c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{cos}(x)\\lim_{h \\to 0}\\frac{\\text{cos}(h)-1}{h}-\\text{sen}(x)\\lim_{h \\to 0}\\frac{\\text{sen}(h)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"383\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u901a\u8fc7\u65e0\u7a77\u5c0f\u5f53\u91cf\u8ba1\u7b97\u6781\u9650\uff0c\u6211\u4eec\u5f97\u51fa\u7b2c\u4e00\u4e2a\u6781\u9650\u4e3a 0\uff0c\u7b2c\u4e8c\u4e2a\u6781\u9650\u4e3a 1\u3002\u56e0\u6b64\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-f0c2ed1188b80356d05d6188fab5ca47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\text{cos}(x)\\cdot 0-\\text{sen}(x)\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"223\" 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-9f33ae6c9b18e01ba654772f22cab6d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=-\\text{sen}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u81f3\u6b64\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86\u4f59\u5f26\u51fd\u6570\u5bfc\u6570\u7684\u516c\u5f0f\uff0c\u56e0\u6b64\u7b49\u5f0f\u5f97\u5230\u8bc1\u660e\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bfc\u51fa\u4f59\u5f26\u51fd\u6570\uff08\u516c\u5f0f\uff09\u3002\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4f59\u5f26\u51fd\u6570\u5bfc\u6570\u7684\u793a\u4f8b\uff0c\u5e76\u901a\u8fc7\u9010\u6b65\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u5411 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%94%b1%e4%bd%99%e5%bc%a6%e5%af%bc%e5%87%ba\/\"> <span class=\"screen-reader-text\">\u4f59\u5f26\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-30","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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