{"id":381,"date":"2023-07-03T07:22:34","date_gmt":"2023-07-03T07:22:34","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%94%b1%e4%bd%99%e5%89%b2%e5%af%bc%e5%87%ba\/"},"modified":"2023-07-03T07:22:34","modified_gmt":"2023-07-03T07:22:34","slug":"%e7%94%b1%e4%bd%99%e5%89%b2%e5%af%bc%e5%87%ba","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%94%b1%e4%bd%99%e5%89%b2%e5%af%bc%e5%87%ba\/","title":{"rendered":"\u4f59\u5272\u7684\u5bfc\u6570"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\uff08\u516c\u5f0f\uff09\u7684\u4f59\u5272\u3002\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u9010\u6b65\u89e3\u51b3\u4f59\u5272\u5bfc\u6570\u7684\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u60a8\u5c06\u80fd\u591f\u770b\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=\"formula-de-la-derivada-de-la-cosecante\"><\/span>\u4f59\u5272\u5bfc\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>x \u7684\u4f59\u5272\u5bfc\u6570\u7b49\u4e8e\u51cf\u53bb x \u7684\u4f59\u5f26\u9664\u4ee5 x \u7684\u5e73\u65b9\u6b63\u5f26\u6240\u5f97\u7684\u5546\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19e966c85664331b8b6c87860849678d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"416\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4f7f\u7528\u4e09\u89d2\u516c\u5f0f\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5c06 x \u7684\u4f59\u5272\u7684\u5bfc\u6570\u5b9a\u4e49\u4e3a\u51cf\u53bb x \u7684\u4f59\u5207\u4e58\u4ee5 x \u7684\u4f59\u5272\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-e66d4cc483a3f2c40401bf2e34fa54c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=-\\cfrac{\\text{cos}(x)}{\\text{sen}^2(x)}=-\\cfrac{\\text{cos}(x)}{\\text{sen}(x)}\\cdot \\cfrac{1}{\\text{sen}(x)}=-\\text{cot}(x)\\cdot \\text{cosec}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u6211\u4eec\u5e94\u7528\u94fe\u5f0f\u6cd5\u5219\uff0c<strong>\u51fd\u6570\u4f59\u5272\u7684\u5bfc\u6570<\/strong>\u51cf\u53bb\u51fd\u6570\u5bfc\u6570\u4e58\u4ee5\u51fd\u6570\u4f59\u5f26\u7684\u4e58\u79ef\uff0c\u518d\u9664\u4ee5\u51fd\u6570\u7684\u6b63\u5f26\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7528\u4e8e\u5bfc\u51fa\u51fd\u6570\u4f59\u5272\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\/derive-de-la-formule-cosecante.webp\" alt=\"\u7531\u4f59\u5272\u516c\u5f0f\u63a8\u5bfc\u51fa\u6765\" class=\"wp-image-2527\" width=\"398\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-la-cosecante\"><\/span>\u4f59\u5272\u5bfc\u6570\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e86\u89e3\u4e86\u4f59\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\u4e4b\u540e\uff0c\u6211\u4eec\u73b0\u5728\u5c06\u7ed9\u51fa\u51e0\u4e2a\u4f8b\u5b50\u3002\u8fd9\u6837\u60a8\u5c31\u53ef\u4ee5\u51c6\u786e\u5730\u770b\u5230\u51fd\u6570\u7684\u4f59\u5272\u662f\u5982\u4f55\u5bfc\u51fa\u7684\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-la-cosecante-de-2x\"><\/span>\u793a\u4f8b 1\uff1a2x \u4f59\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 \u4f59\u5272\u7684\u5bfc\u6570\u662f\u591a\u5c11\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-44aef07389e7b7d69f4ecf9e46660838_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f59\u5272\u81ea\u53d8\u91cf\u51fd\u6570\u4e0ex\u4e0d\u540c\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u5c06\u4f59\u5272\u5bfc\u6570\u6cd5\u5219\u4e0e\u94fe\u5f0f\u6cd5\u5219\u7ed3\u5408\u4f7f\u7528\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\uff0c\u8981\u6c42\u8fd9\u4e2a\u4e09\u89d2\u51fd\u6570\u7684\u5bfc\u6570\uff0c\u53ea\u9700\u4ee3\u5165\u524d\u9762\u516c\u5f0f\u4e2d\u7684\u503c\u5373\u53ef\uff1a\u5728\u4f59\u5f26\u548c\u6b63\u5f26\u53c2\u6570\u4e2d\u6211\u4eec\u653e\u5165 2x\uff0cu&#8217; \u5bf9\u5e94\u4e8e 2x \u7684\u5bfc\u6570\uff0c\u5373 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-8607025c53ca3c1a2c5e05e908d61bc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2\\cdot \\text{cos}(2x)}{\\text{sen}^2(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"446\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-la-cosecante-de-x-al-cuadrado\"><\/span>\u793a\u4f8b 2\uff1ax \u5e73\u65b9\u4f59\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\u4f59\u5272\u7684\u5bfc\u6570\u662f\u591a\u5c11\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-dc9de51c8f24850940b40de616428dd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u8be5\u4e09\u89d2\u51fd\u6570\u7684\u5bfc\u6570\u53ef\u4ee5\u4f7f\u7528\u4f59\u5272\u5bfc\u6570\u516c\u5f0f\u6c42\u89e3\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> x \u5e73\u65b9\u7684\u5bfc\u6570\u4e3a 2x\uff0c\u56e0\u6b64 x \u7684\u4f59\u5272\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-0a6b69e1f9851904ec2fc68bffeedc64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{2x\\cdot \\text{cos}(x^2)}{\\text{sen}^2(x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"454\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-la-cosecante-al-cubo-de-una-funcion-exponencial\"><\/span>\u793a\u4f8b 3\uff1a\u6307\u6570\u51fd\u6570\u7684\u4e09\u6b21\u4f59\u5272\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-8bd5c47e8cd53ab52d3d30f55f898490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}^3(e^{5x})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"142\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u65e0\u8bba\u51fd\u6570\u7684\u53c2\u6570\u662f\u4ec0\u4e48\uff0c\u51fd\u6570\u4f59\u5272\u7684\u5bfc\u6570\u89c4\u5219\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-b15904d25f18713a0d713cda3ab2bfe1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=-\\cfrac{u'\\cdot \\text{cos}(u)}{\\text{sen}^2(u)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"435\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4f46\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u590d\u5408\u51fd\u6570\uff0c\u56e0\u4e3a\u4f59\u5272\u88ab\u63d0\u9ad8\u5230\u4e09\uff0c\u800c\u4e14\uff0c\u5728\u5b83\u7684\u53c2\u6570\u4e2d\u6709\u4e00\u4e2a\u6307\u6570\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u5bf9\u6574\u4e2a\u51fd\u6570\u6c42\u5bfc\uff0c\u6211\u4eec\u9700\u8981\u591a\u6b21\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-9ac2ce49dfcba1b7f27696dba0a2decb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle f'(x)&amp; = 3\\text{cosec}^2(e^{5x})\\cdot\\left(-\\frac{5e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\right)\\\\[1.5ex]&amp;=-\\frac{-15\\text{cosec}^2(e^{5x})\\cdot e^{5x}\\cdot \\text{cos}(e^{5x})}{\\text{sen}^2(e^{5x})}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"316\" 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-la-cosecante\"><\/span>\u89e3\u51b3\u4e86\u4f59\u5272\u5bfc\u6570\u7684\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a8\u5bfc\u4ee5\u4e0b\u4f59\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-9929e2437b0ed56c3510e3e0e66745c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\text{cosec}(x^4-2x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"203\" 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-90abcf0539f30dc6fc72414bfc74510f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\text{cosec}(x^3+e^x-10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"232\" 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-86a2ea6229cced9086f8baba7afd49dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\text{cosec}\\bigl(\\ln(x^3+7x^2)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" 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-45cdf124149223f4a3bec4984dc3ad3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{cosec}\\bigl(\\text{arccos}(x^7)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"217\" 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-45ae6ef998d8ab0c30309fe521b0bafc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{cosec}\\left(\\sqrt{9x^2-4x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"226\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1fb207498fc67f62e6c30a0baecc9549_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f('x)=-\\cfrac{(4x^3-4x)\\cdot \\text{cos}(x^4-2x^2)}{\\text{sen}^2(x^4-2x^2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"303\" 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-d42a3db78890f44f3cac95685ab9362e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f('x)=-\\cfrac{(3x^2+e^x)\\cdot \\text{cos}(x^3+e^x-10)}{\\text{sen}^2(x^3+e^x-10)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"329\" 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-32dde68d2a11ef6a05d483b26f0a98ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp; =-\\cfrac{\\cfrac{3x^2+14x}{x^3+7x^2}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{\\cfrac{3x+14}{x^2+7x}\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{\\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\\\[1.5ex] &amp;= -\\cfrac{(3x+14)\\cdot \\text{cos}\\bigl(\\ln(x^3+7x^2)\\bigr)}{(x^2+7x)\\cdot \\text{sen}^2\\bigl(\\ln(x^3+7x^2)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"333\" 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-b2bea25dae467cefdcc1bd48e8d9bc88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{D) }f'(x)&amp; =-\\cfrac{-\\cfrac{7x^6}{\\sqrt{1-\\left(x^7\\right)^2}}\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =-\\cfrac{(-7x^6)\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\\\[1.5ex] &amp; =\\cfrac{7x^6\\cdot \\text{cos}\\bigl(\\text{arccos}(x^7)\\bigr)}{\\left(\\sqrt{1-x^{14}}\\right)\\cdot \\text{sen}^2\\bigl(\\text{arccos}(x^7)\\bigr)}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"240\" width=\"348\" 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-eb70e1d7b6f2ce2636934b235904861f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\text{E) }f'(x)&amp; =-\\cfrac{\\cfrac{18x-4}{2\\cdot\\sqrt{9x^2-4x}} \\cdot \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{\\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)}\\\\[1.5ex] &amp;=-\\cfrac{(18x-4)\\cdot  \\text{cos}\\left(\\sqrt{9x^2-4x}\\right)}{2\\sqrt{9x^2-4x}\\cdot \\text{sen}^2\\left(\\sqrt{9x^2-4x}\\right)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"165\" width=\"352\" 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-de-la-cosecante\"><\/span>\u4f59\u5272\u5bfc\u6570\u516c\u5f0f\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u6f14\u793a\u4f59\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u4e0e\u5176\u4ed6\u6f14\u793a\u4e0d\u540c\uff0c\u5728\u672c\u4f8b\u4e2d\uff0c\u6211\u4eec\u4e0d\u4f1a\u4f7f\u7528\u5b9a\u4e49\u5bfc\u6570\u7684\u6781\u9650\uff0c\u800c\u662f\u4ece\u4f59\u5272\u7684\u6570\u5b66\u5b9a\u4e49\u5f00\u59cb\u3002<\/p>\n<p>\u5728\u4ee3\u6570\u4e0a\uff0c\u4f59\u5272\u4e09\u89d2\u51fd\u6570\u662f\u6b63\u5f26\u7684\u4e58\u6cd5\u9006\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-6ac8ff987dcebfb971915b090d8dc455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosec}(x)=\\cfrac{1}{\\text{sen}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"196\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5546\u89c4\u5219\u6c42\u4f59\u5272\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-956e802336ed97943a839dbc059a168a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{0\\cdot \\text{sen}(x)-1\\cdot \\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"227\" 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-d26ab733704d285da0ec63f0901330b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\cfrac{-\\text{cos}(x)}{\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u53ea\u6709\u901a\u8fc7\u5e94\u7528\u9664\u6cd5\u5bfc\u6570\u7684\u89c4\u5219\uff0c\u6211\u4eec\u624d\u80fd\u5f97\u51fa\u4f59\u5272\u5bfc\u6570\u7684\u516c\u5f0f\u3002\u7531\u4e8e\u5546\u7684\u5bfc\u6570\u5df2\u7ecf\u88ab\u8bc1\u660e\uff08\u60a8\u53ef\u4ee5\u5728\u4ee5\u4e0b\u94fe\u63a5\u4e2d\u770b\u5230\u5b83\uff09\uff0c\u4f59\u5272\u5bfc\u6570\u89c4\u5219\u4e5f\u88ab\u8bc1\u660e\u3002<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u89c1\uff1a<\/strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u9664\u5546\u7684\u5bfc\u6570\/\">\u5546\u5bfc\u6570\u7684\u8bc1\u660e<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5c06\u89e3\u91ca\u5982\u4f55\u5bfc\u51fa\u51fd\u6570\uff08\u516c\u5f0f\uff09\u7684\u4f59\u5272\u3002\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u9010\u6b65\u89e3\u51b3\u4f59\u5272\u5bfc\u6570\u7684\u7ec3\u4e60\u3002\u6700\u540e\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u6b64\u7c7b\u4e09\u89d2 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%94%b1%e4%bd%99%e5%89%b2%e5%af%bc%e5%87%ba\/\"> <span class=\"screen-reader-text\">\u4f59\u5272\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-381","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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