{"id":32,"date":"2023-09-17T11:02:19","date_gmt":"2023-09-17T11:02:19","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e9%80%86%e6%ad%a3%e6%8e%a5-1-%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-09-17T11:02:19","modified_gmt":"2023-09-17T11:02:19","slug":"%e9%80%86%e6%ad%a3%e6%8e%a5-1-%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e9%80%86%e6%ad%a3%e6%8e%a5-1-%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u9006\u6b63\u63a5\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u305f\u308a\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u3044\u3066\u7df4\u7fd2\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u3082\u793a\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-derivada-del-arcotangente\"><\/span>\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>x \u306e\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306f\u30011 \u306e 1 \u306b x \u306e 2 \u4e57\u3092\u52a0\u3048\u305f\u3082\u306e\u3067\u3059\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-cdeb5e29b862b8b9d5bc9f4c2c747106_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{1}{1+x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u95a2\u6570\u306e\u9006\u6b63\u63a5\u306e\u5fae\u5206\u5024<\/strong>\u306f\u3001\u305d\u306e\u95a2\u6570\u306e\u5fae\u5206\u5024\u3092 1 \u3067\u5272\u3063\u305f\u5546\u306b\u3001\u305d\u306e\u95a2\u6570\u306e 2 \u4e57\u3092\u52a0\u3048\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u95a2\u6570\u306f au \u3067\u8868\u3055\u308c\u308b\u305f\u3081\u3001\u3053\u308c\u306f\u95a2\u6570 u \u306e\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002 <\/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-arctangente.webp\" alt=\"\u9006\u6b63\u63a5\u304b\u3089\u5c0e\u51fa\" class=\"wp-image-1997\" width=\"389\" height=\"296\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306f\u3001\u9006\u6b63\u5f26\u304a\u3088\u3073\u9006\u4f59\u5f26\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3068\u975e\u5e38\u306b\u3088\u304f\u4f3c\u3066\u3044\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-del-arcotangente\"><\/span>\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u304c\u308f\u304b\u3063\u305f\u3089\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u4e09\u89d2\u95a2\u6570\u5c0e\u95a2\u6570\u306e\u3044\u304f\u3064\u304b\u306e\u4f8b\u306e\u5c0e\u51fa\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3053\u3046\u3059\u308b\u3053\u3068\u3067\u3001\u95a2\u6570\u306e\u9006\u6b63\u63a5\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u306e\u304b\u3092\u7406\u89e3\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-del-arcotangente-de-2x\"><\/span>\u4f8b 1: 2x \u306e\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\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-3c8877ac889f77baa22f66d4b2568418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b21\u306e\u5f0f\u3092\u9069\u7528\u3057\u3066\u5c0e\u95a2\u6570\u3092\u89e3\u304d\u307e\u3059\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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> 2x \u306e\u5fae\u5206\u5024\u306f 2 \u306a\u306e\u3067\u30012x \u306e\u9006\u6b63\u63a5\u5fae\u5206\u5024\u306f 2 \u306b 1 \u3092\u52a0\u3048\u305f\u3082\u306e\u306b 2x \u306e 2 \u4e57\u3092\u52a0\u3048\u305f\u3082\u306e\u306b\u306a\u308a\u307e\u3059\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-f2a5ff151a4471bb769c46ac896ee0ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(2x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2}{1+(2x)^2}}=\\cfrac{2}{1+ 4x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"518\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-del-arcotangente-de-x-al-cuadrado\"><\/span>\u4f8b 2: x \u306e 2 \u4e57\u306e\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\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-3f62897c299972bd734ffe87b6d28e84_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u4f8b\u306e\u5c0e\u95a2\u6570\u306e\u7d50\u679c\u3092\u6c42\u3081\u308b\u306b\u306f\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570 x <sup>2<\/sup>\u306e\u5c0e\u95a2\u6570\u306f 2x \u3067\u3042\u308b\u305f\u3081\u3001x \u306e\u9006\u6b63\u63a5\u306e 2 \u4e57\u306e\u5c0e\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\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-4518d6b8df16464b2a763eb7d736504d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(x^2) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{2x}{1+\\left(x^2\\right)^2}=\\cfrac{2x}{1+x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"507\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-del-arcotangente-del-seno-de-x\"><\/span>\u4f8b 3: x \u306e\u30b5\u30a4\u30f3\u306e\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\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-72df0a729eefc917694a84ecccd4a959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}\\bigl(\\text{sen}(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"170\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u8ad6\u7406\u7684\u306b\u306f\u3001\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u5bfe\u5fdc\u3059\u308b\u5f0f\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\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-6c6546edbf0ff2d0ccba20a7fac11b89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}(u) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{u'}{1+u^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"404\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u5408\u6210\u95a2\u6570\u304c\u3042\u308b\u305f\u3081\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u9023\u9396\u898f\u5247\u3092\u9069\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\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-f3897b362bb6b4681404918f45e91565_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{arctan}\\bigl(\\text{sen}(x)\\bigr) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} f'(x)=\\cfrac{\\text{cos}(x)}{1+\\text{sen}^2(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"482\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-derivada-del-arcotangente\"><\/span>\u9006\u6b63\u63a5\u306e\u5fae\u5206\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u9006\u6b63\u63a5\u95a2\u6570\u3092\u5c0e\u51fa\u3057\u307e\u3059\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-23cb449bba097b71c6154e6bfd755940_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=\\text{arctan}(x^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" 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-8ec295f2cfb72911775d2bc47d379e11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=\\cfrac{\\text{arctan}(3x^4)}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"175\" 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-5e54c5dc5ee8464186009da410740df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=\\text{arctan}(x^5-3x^3+10)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"252\" 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-b63b4e04e749c7b7d4cfecca4391eee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\text{arctan}^3(4x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"181\" 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-6c72a415d8c2e54870c4dc2e92344cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\text{arctan}\\bigl(\\ln(x)\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"185\" 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-4fad4c5f97c1492b8ad5df06b165d2c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\text{arctan}\\left(\\sqrt{x^2+2x}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"227\" 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>\u89e3\u6c7a\u7b56\u3092\u898b\u308b<\/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-effa4065c7c98ae655b2cc5bdf14ca07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=\\cfrac{3x^2}{1+\\left(x^3\\right)^2}=\\cfrac{3x^2}{1+x^6}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"235\" 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-2de05c8d708d379982abc8461f5d8706_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=\\cfrac{12x^3}{2\\left(1+\\left(3x^4\\right)^2\\right)}=\\cfrac{6x^3}{1+9x^8}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"285\" style=\"vertical-align: -30px;\"><\/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-d72faae19f9b5cd7a8d53364bcf9817a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=\\cfrac{5x^4-9x^2}{1+\\left(x^5-3x^3+10\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"248\" 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-ea7d5ff105b7432c2756cdcbf44e311b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=3\\text{arctan}^2(4x^2)\\cdot \\cfrac{8x}{1+\\left(4x^2\\right)^2}=\\cfrac{24x\\cdot\\text{arctan}^2(4x^2)}{1+16x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"453\" 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-6eefb865fce5124f8326d122437c3124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=\\cfrac{\\cfrac{1}{x}}{1+\\bigl(\\ln(x)\\bigr)^2}=\\cfrac{1}{x\\left(1+\\ln^2(x)\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"315\" style=\"vertical-align: -23px;\"><\/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-6faff8aba659922b2cfc784a4f3dae4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{1}{1+\\left(\\sqrt{x^2+2x}\\right)^2}\\cdot \\cfrac{2x+2}{2\\sqrt{x^2+2x}}=\\cfrac{x+1}{\\left(1+x^2+2x\\right)\\sqrt{x^2+2x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"524\" style=\"vertical-align: -33px;\"><\/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-arcotangente\"><\/span>\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306b\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3059\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-88c05a50eddb183a57270676d6ebc5cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\text{arctan}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u307e\u305a\u3001\u9006\u6b63\u63a5\u304c\u6b63\u63a5\u306e\u9006\u95a2\u6570\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u3092\u5229\u7528\u3057\u3066\u3001\u9006\u6b63\u63a5\u3092\u6b63\u63a5\u306b\u5909\u63db\u3057\u307e\u3059\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-e806041dd9dbc7cf01bb34014aa18d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\text{tan}(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u65b9\u7a0b\u5f0f\u306e\u4e21\u8fba\u3092\u5fae\u5206\u3057\u307e\u3059\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-ca9f080338b9ab014e272f81395146ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1=\\cfrac{1}{\\text{cos}^2(y)}\\cdot y'\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"114\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6d88\u53bb\u3057\u3066\u3001&#8217;:<\/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-05c04d0ce365d8bd7848d4923038778c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\text{cos}^2(y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"91\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e00\u65b9\u3001\u57fa\u672c\u7684\u306a\u4e09\u89d2\u95a2\u6570\u306e\u6052\u7b49\u5f0f\u306e\u304a\u304b\u3052\u3067\u3001\u30b5\u30a4\u30f3\u3068\u30b3\u30b5\u30a4\u30f3\u306e\u4e8c\u4e57\u306e\u548c\u306f 1 \u306b\u7b49\u3057\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u524d\u306e\u5f0f\u3092\u5206\u6570\u306b\u5909\u63db\u3067\u304d\u307e\u3059\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-34f7d2ec2a5836c843db8adea73d021f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{sen}^2(y)+\\text{cos}^2(y)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" 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-d5314e15fe7e8ff7c9155906e7725483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\text{cos}^2(y)}{1}=\\cfrac{\\text{cos}^2(y)}{\\text{sen}^2(y)+\\text{cos}^2(y)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"252\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3059\u3079\u3066\u306e\u9805\u3092\u30b3\u30b5\u30a4\u30f3\u306e\u4e8c\u4e57\u3067\u5272\u308a\u307e\u3059\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-39e03a87b9a62ab2db6a56192e44f531_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{\\cfrac{\\text{cos}^2(y)}{\\text{cos}^2(y)}}{\\cfrac{\\text{sen}^2(y)}{\\text{cos}^2(y)}+\\cfrac{\\text{cos}^2(y)}{\\text{cos}^2(y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"96\" width=\"176\" style=\"vertical-align: -44px;\"><\/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-3cf88afedfff6a5c53ffb31df510b4ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\cfrac{\\text{sen}^2(y)}{\\text{cos}^2(y)}+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"70\" width=\"128\" style=\"vertical-align: -44px;\"><\/p>\n<\/p>\n<p>\u30b5\u30a4\u30f3\u3092\u30b3\u30b5\u30a4\u30f3\u3067\u5272\u3063\u305f\u5024\u306f\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306b\u7b49\u3057\u3044\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\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-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 class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db914ed4a068a6dff2598b981b1682d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{\\text{tan}^2(y)+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"126\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u4e0a\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u30bf\u30f3\u30b8\u30a7\u30f3\u30c8\u306f\u5909\u6570 x \u3068\u540c\u7b49\u306a\u306e\u3067\u3001\u5f0f\u3092\u4ee3\u5165\u3057\u3066\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\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-61292316edd6cef99a6135989713cd22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y'=\\cfrac{1}{x^2+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"88\" style=\"vertical-align: -14px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u95a2\u6570\u306e\u9006\u6b63\u63a5\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u305f\u308a\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u3044\u3066\u7df4\u7fd2\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u8a3c\u660e\u3082\u793a\u3057\u307e\u3059\u3002 \u9006\u6b63\u63a5\u306e\u5c0e\u95a2 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e9%80%86%e6%ad%a3%e6%8e%a5-1-%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u9006\u6b63\u63a5\u306e\u5c0e\u95a2\u6570<\/span> \u3082\u3063\u3068\u8aad\u3080 &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-32","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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