{"id":36,"date":"2023-09-17T11:00:46","date_gmt":"2023-09-17T11:00:46","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e9%99%a4%e7%ae%97%e5%95%86%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-09-17T11:00:46","modified_gmt":"2023-09-17T11:00:46","slug":"%e9%99%a4%e7%ae%97%e5%95%86%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e9%99%a4%e7%ae%97%e5%95%86%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u5546\uff08\u307e\u305f\u306f\u9664\u7b97\uff09\u306e\u5c0e\u95a2\u6570"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u30012 \u3064\u306e\u95a2\u6570\u304b\u3089\u5546 (\u307e\u305f\u306f\u9664\u7b97) \u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u95a2\u6570\u306e\u5546\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u304c\u3042\u308a\u3001\u3055\u3089\u306b\u3001\u5272\u308a\u7b97\u306e\u5c0e\u95a2\u6570\u306b\u3064\u3044\u3066\u6bb5\u968e\u7684\u306a\u6f14\u7fd2\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-un-cociente\"><\/span>\u5546\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u95a2\u6570\u306e\u4fc2\u6570 (\u307e\u305f\u306f\u9664\u7b97) \u306e\u5c0e\u95a2\u6570\u306f\u3001<\/strong>\u5206\u6bcd\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u9ad8\u3044\u5206\u6bcd\u95a2\u6570\u306e 2 \u4e57\u3067\u5272\u3063\u305f\u5206\u5b50\u95a2\u6570\u3088\u308a\u3082\u5c0f\u3055\u3044\u3001\u5206\u6bcd\u95a2\u6570\u306b\u3088\u308b\u5206\u5b50\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3068\u540c\u3058\u3067\u3059\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-quotient-de-division-derivee.webp\" alt=\"\u9664\u7b97\u307e\u305f\u306f\u5546\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\" class=\"wp-image-2194\" width=\"326\" height=\"304\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p>\u3054\u89a7\u306e\u3068\u304a\u308a\u3001\u5546 (\u307e\u305f\u306f\u5272\u308a\u7b97) \u306e\u5c0e\u95a2\u6570\u306b\u30eb\u30fc\u30eb\u3092\u9069\u7528\u3059\u308b\u3068\u3001\u5fae\u5206\u5f8c\u3082\u5206\u6570\u304c\u6b8b\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u5206\u5b50\u306b\u306f 2 \u3064\u306e\u4e57\u7b97\u3068 1 \u3064\u306e\u6e1b\u7b97\u304c\u3042\u308a\u3001\u5206\u6bcd\u306f 2 \u4e57\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-derivadas-de-cocientes\"><\/span>\u5546\u306e\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>2 \u3064\u306e\u95a2\u6570\u306e\u5546\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u8aac\u660e\u3057\u307e\u3057\u305f\u3002\u6b21\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u6f14\u7b97\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002\u95a2\u6570\u5546\u306e\u5c0e\u51fa\u65b9\u6cd5\u304c\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u306f\u3001\u30b3\u30e1\u30f3\u30c8\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u8cea\u554f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u4f8b1<\/h3>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u4e09\u89d2\u95a2\u6570\u3067\u5272\u3063\u305f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\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-9d260d4cdca9f28e43607a9c1e7b3404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{3x^2+4x}{\\text{sen}(2x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"128\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> 2 \u3064\u306e\u7570\u306a\u308b\u95a2\u6570\u306e\u9664\u7b97\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306b\u5404\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u500b\u5225\u306b\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-21\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-24719cd47158514d54e16f4994a1c2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (3x^2+4x)=6x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"180\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-093fb274a2a393453833ed572dc1bc62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\text{sen}(2x)=2\\text{cos}(2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"171\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u95a2\u6570\u5168\u4f53\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-65ce4673f3ad5a4c09a9b2e7c611821d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{3x^2+4x}{\\text{sen}(2x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{(6x+4)\\cdot\\text{sen}(2x)-(3x^2+4x)\\cdot 2\\text{cos}(2x)}{\\text{sen}^2(2x)}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"380\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u4f8b 2<\/h3>\n<p>\u3053\u306e\u5834\u5408\u3001\u5b9a\u6570\u3092\u95a2\u6570\u3067\u5272\u3063\u305f\u5c0e\u95a2\u6570\u3092\u6c42\u3081\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-e7d5ddfdf95f11b94783ca40437e371a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{10}{x^2+3x-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"150\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u4e0a\u3067\u898b\u305f\u3088\u3046\u306b\u30012 \u3064\u306e\u7570\u306a\u308b\u95a2\u6570\u306e\u9664\u7b97\u306e\u5c0e\u95a2\u6570\u306e\u30eb\u30fc\u30eb\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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u5c0e\u95a2\u6570\u3092\u5225\u3005\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-24\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-191c03d69e261059308133b99f87bf1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 10=0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c63da81dbf763b0a24cf929aef024c51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^2+3x-9)=2x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"201\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001\u6574\u6570\u306e\u9664\u7b97\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\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-8f8bdea77dc91b1aff40695511593e86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{10}{x^2+3x-9}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{0\\cdot (x^2+3x-9)-10\\cdot (2x+3)}{\\left(x^2+3x-9\\right)^2}=\\cfrac{-20x+30}{\\left(x^2+3x-9\\right)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"441\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5b9f\u969b\u3001\u5206\u5b50\u306b\u5b9a\u6570\u3092\u95a2\u6570\u3067\u5272\u3063\u305f\u5834\u5408\u3001\u5b9a\u6570\u306e\u5c0e\u95a2\u6570\u306f\u5e38\u306b 0 \u306b\u306a\u308b\u305f\u3081\u3001\u76f4\u63a5\u5fae\u5206\u3059\u308b\u516c\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u516c\u5f0f\u306f\u5e38\u306b true \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-1f0bd615634f5205f91674f96f5c2514_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{taronjaquadreejemplo}{HTML}{FF9800}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=taronjaquadreejemplo,      boxrule=1.1pt, boxsep=2mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2mm}{-2mm}{0mm}{taronjaquadreejemplo!20!white,} ]}]{equation*}      \\begin{array}{c}z(x)=\\cfrac{k}{f(x)} \\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{-k\\cdot f'(x)}{\\bigl(f(x)\\bigr)^2}\\end{array} \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u4f8b 3<\/h3>\n<p>\u3053\u306e\u6f14\u7fd2\u3067\u306f\u30012 \u3064\u306e\u591a\u9805\u5f0f\u306e\u5546\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-59b390fee61ab3c2cbb4dc2230386658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"127\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u5c0e\u95a2\u6570\u3092\u89e3\u304f\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306a 2 \u3064\u306e\u7570\u306a\u308b\u95a2\u6570\u306e\u5546\u306e\u5c0e\u95a2\u6570\u306e\u30eb\u30fc\u30eb\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-fc09ff88e92ee46b5c98d6fc81a5d5a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=\\cfrac{f(x)}{g(x)}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] z'(x)=\\cfrac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"139\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u5206\u5b50\u591a\u9805\u5f0f\u3068\u5206\u6bcd\u591a\u9805\u5f0f\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-27\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-39e82139a124bf031f31b84007bcb923_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (x^3+4x^2)=3x^2+8x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"196\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-73db77f7639fc8b4cc305fbbb2b1cf2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ (5x^2-8)=10x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"148\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u591a\u7fa9\u8a9e\u306e\u9664\u7b97\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-065ad49556f264b4cfb505522ad7566b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}f(x)=\\cfrac{x^3+4x^2}{5x^2-8}\\\\[2.5ex]\\color{orange}\\bm{\\downarrow}\\\\[1.5ex] f'(x)=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"137\" width=\"373\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u5f8c\u306b\u3001\u6f14\u7b97\u3092\u5b9f\u884c\u3057\u3066\u3001\u53ef\u80fd\u306a\u9650\u308a\u5206\u6570\u3092\u5358\u7d14\u5316\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-af3f7cb513883d1fa5dadca23701c19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}f'(x)&amp;=\\cfrac{(3x^2+8x)\\cdot (5x^2-8)-(x^3+4x^2)\\cdot 10x}{\\left(5x^2-8\\right)^2}\\\\[2ex]&amp;=\\cfrac{15x^4-24x^2+40x^3-64x-10x^4-40x^3}{25x^4+64-80x^2}\\\\[2ex]&amp;=\\cfrac{5x^4-24x^2-64x}{25x^4-80x^2+64}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"178\" width=\"379\" 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-un-cociente\"><\/span>\u5546\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\u95a2\u6570\u306e\u5206\u5272\u3092\u5c0e\u304d\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-e6244d0e6cfcb8c4b82806d40cab93fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) }f(x)=\\cfrac{9x^2+5x}{6x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"154\" 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-e94071c6dc40cd4a7280be617cdddd3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f(x)=\\cfrac{19}{2x^2-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" 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-214e8c32a9ffb1c37f164935c3ad6bfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) }f(x)=\\cfrac{8x^3-4x^2+3x}{e^{4x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"202\" 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-a83ff4c06137279870296a80b12b0cec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f(x)=\\cfrac{\\text{cos}(x^2)}{\\text{sen}(6x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"144\" 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-4bed0ff9464adb5897528d5b47ed477c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) }f(x)=\\cfrac{\\ln(x^3+4)}{\\left(4x^2-3x\\right)^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"174\" 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-74ddf8caa494c9a60dcbfc9d57c90d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) }f(x)=\\cfrac{\\sqrt{x^2+4x}}{5^{x^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"158\" style=\"vertical-align: -13px;\"><\/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-26b0af84dd46ca29727eee97380b4ca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{A) }f'(x)&amp;=\\cfrac{(18x+5)\\cdot 6x^3-(9x^2+5x)\\cdot 18x^2}{\\left(6x^3\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{108x^4+30x^3-162x^4-90x^3}{36x^6}\\\\[1.5ex]&amp;=\\cfrac{-54x^4-60x^3}{36x^6}\\\\[1.5ex]&amp;=\\cfrac{-9x-10}{6x^3}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"225\" width=\"354\" 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-97bee45dee6ebba49cd8a9822ef70308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) }f'(x)=\\cfrac{-19\\cdot 4x}{\\left(2x^2-2\\right)^2}=\\cfrac{-76x}{\\left(2x^2-2\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"273\" 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-11f9c8fda61edb1ce51bd33e022a0a24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{C) }f'(x)&amp;=\\cfrac{(24x^2-8x+3)e^{4x}-(8x^3-4x^2+3x)\\cdot 4e^{4x}}{\\left(e^{4x}\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{e^{4x}(24x^2-8x+3-32x^3+16x^2-12x)}{e^{8x}}\\\\[1.5ex]&amp;=\\cfrac{-32x^3+40x^2-20x+3}{e^{4x}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"431\" 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-da9da045ccfc03ecc1d9d44e1ea9caee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) }f'(x)=\\cfrac{-2x\\text{sen}(x^2)\\cdot\\text{sen}(6x)-\\text{cos}(x^2)\\text{cos}(6x)\\cdot 6}{\\text{sen}^2(6x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"414\" 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-ec87daa1a463bacd5a42a1b16e826449_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{E) }f'(x)&amp;=\\cfrac{\\cfrac{3x^2}{x^3+4}\\cdot\\left(4x^2-3x\\right)^3-\\ln(x^3+4)\\cdot 3\\left(4x^2-3x\\right)^2\\cdot (8x-3) }{\\left(\\left(4x^2-3x\\right)^3\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{\\cfrac{3x^2}{x^3+4}\\cdot\\left(4x^2-3x\\right)^3-\\ln(x^3+4)\\cdot 3\\left(4x^2-3x\\right)^2\\cdot (8x-3) }{\\left(4x^2-3x\\right)^6}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"170\" width=\"535\" 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-bef2b22482e39cea7e82047c0d9911b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\text{F) }f'(x)&amp;=\\cfrac{\\cfrac{2x+4}{2\\sqrt{x^2+4x}}\\cdot 5^{x^2} - \\sqrt{x^2+4x}\\cdot 5^{x^2}\\cdot \\ln(5) \\cdot 2x }{\\left(5^{x^2}\\right)^2}\\\\[1.5ex]&amp;=\\cfrac{\\cfrac{2x+4}{2\\sqrt{x^2+4x}}\\cdot 5^{x^2} - \\sqrt{x^2+4x}\\cdot 5^{x^2}\\cdot \\ln(5) \\cdot 2x }{5^{2x^2}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"155\" width=\"424\" 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-de-un-cociente\"><\/span>\u5546\u306e\u5c0e\u95a2\u6570\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001\u9664\u7b97\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u884c\u3046\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306a\u5c0e\u95a2\u6570\u306e\u4e00\u822c\u7684\u306a\u5b9a\u7fa9\u3092\u4f7f\u7528\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-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> <em>z \u3092<\/em>2 \u3064\u306e\u7570\u306a\u308b\u95a2\u6570\u306e\u9664\u7b97\u3068\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-83357f61a7cd6587a3fd5e5348b056fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=\\cfrac{f(x)}{g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"94\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6b21\u306b\u3001\u6570\u5b66\u7684\u5b9a\u7fa9\u3092\u9069\u7528\u3057\u305f\u95a2\u6570<em>z<\/em>\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-db6545eb9e109966a362acf510f101a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\cfrac{f(x+h)}{g(x+h)}-\\cfrac{f(x)}{g(x)}}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"223\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u306e\u5206\u5b50\u304b\u3089\u5206\u6570\u306e\u5f15\u304d\u7b97\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-f9ec617a63f72bd4215ccb2b2998525e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{\\cfrac{f(x+h)\\cdot g(x)}{g(x+h)\\cdot g(x)}-\\cfrac{f(x)\\cdot g(x+h)}{g(x)\\cdot g(x+h)}}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"347\" style=\"vertical-align: -13px;\"><\/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-f8a9e6382fd7033298df2e7955ccd9fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x)-f(x)\\cdot g(x+h)}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"343\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u65b9\u7a0b\u5f0f\u306b\u52a0\u7b97\u9805\u3068\u6e1b\u7b97\u9805\u3092\u8ffd\u52a0\u3057\u3066\u3082\u3001\u65b9\u7a0b\u5f0f\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u9032\u3080\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-8581512accedfadade2e1bbbeec84855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{f(x+h)\\cdot g(x)\\color{orange}\\bm{-f(x)\\cdot g(x)}\\color{black}-f(x)\\cdot g(x+h)\\color{orange}\\bm{+f(x)\\cdot g(x)}\\color{black}}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"720\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5171\u901a\u56e0\u6570\u3092\u62bd\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-b8f9b502b411bb77acebc63c00972053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{g(x)\\bigl[f(x+h)-f(x)\\bigr]-f(x)\\bigl[g(x+h)-g(x)\\bigr]}{h\\cdot g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"457\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u5206\u6570\u306e\u6027\u8cea\u3092\u4f7f\u7528\u3057\u3066\u9805<em>h<\/em>\u3092\u5206\u6bcd\u304b\u3089\u5206\u5b50\u306b\u79fb\u52d5\u3057\u3066\u307f\u307e\u3057\u3087\u3046\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-74338b745f98dd32abeea2df50b88ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\lim_{h \\to 0}\\frac{g(x)\\cdot \\cfrac{f(x+h)-f(x)\\cdot g(x)}{h}-f(x)\\cdot\\cfrac{g(x+h)-g(x)}{h}}{g(x)\\cdot g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"503\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u9650\u754c\u306e\u7279\u6027\u3092\u9069\u7528\u3057\u3066\u65b9\u7a0b\u5f0f\u3092\u5909\u5f62\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-a699ddaf78abfcfbd1aa3993b6a0b033_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}\\cfrac{f(x+h)-f(x)\\cdot g(x)}{h}-f(x)\\cdot\\lim_{h \\to 0}\\cfrac{g(x+h)-g(x)}{h}}{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"535\" style=\"vertical-align: -25px;\"><\/p>\n<\/p>\n<p>\u5206\u5b50\u306e\u6975\u9650\u306f\u3001\u5404\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u306b\u6b63\u78ba\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\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-8735d5a5a43fa63c27443c2fe34a1530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot f'(x)-f(x)\\cdot g'(x)}{g(x)\\cdot \\displaystyle\\lim_{h \\to 0}g(x+h)}\" title=\"Rendered by QuickLaTeX.com\" height=\"51\" width=\"257\" style=\"vertical-align: -25px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u306e\u5206\u6bcd\u306e\u6975\u9650\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-1ef05117a36f586b6c8441b829bd4c42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{g(x)\\cdot f'(x)-f(x)\\cdot g'(x)}{g(x)\\cdot g(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"257\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u95a2\u6570\u306e\u5546\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u304c\u793a\u3055\u308c\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-85517a8cdcfda040b304fbdabe67a5fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f'(x)=\\frac{f'(x)\\cdot g(x)-f(x)\\cdot g'(x)}{\\bigl(g(x)\\bigr)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"257\" style=\"vertical-align: -23px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u30012 \u3064\u306e\u95a2\u6570\u304b\u3089\u5546 (\u307e\u305f\u306f\u9664\u7b97) \u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u95a2\u6570\u306e\u5546\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u304c\u3042\u308a\u3001\u3055\u3089\u306b\u3001\u5272\u308a\u7b97\u306e\u5c0e\u95a2\u6570\u306b\u3064\u3044\u3066\u6bb5\u968e\u7684\u306a\u6f14\u7fd2\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5546\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f \u95a2\u6570\u306e\u4fc2\u6570 (\u307e\u305f\u306f\u9664\u7b97) \u306e\u5c0e &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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