{"id":33,"date":"2023-09-17T11:02:01","date_gmt":"2023-09-17T11:02:01","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e5%92%8c%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/"},"modified":"2023-09-17T11:02:01","modified_gmt":"2023-09-17T11:02:01","slug":"%e5%92%8c%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e5%92%8c%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/","title":{"rendered":"\u5408\u8a08\u304b\u3089\u5c0e\u51fa"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\u95a2\u6570\u306e\u548c\uff08\u516c\u5f0f\uff09\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u548c\u306e\u5fae\u5206\u306e\u4f8b\u3092\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u548c\u306e\u5fae\u5206\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u3066\u7df4\u7fd2\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u5408\u8a08\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-derivada-de-una-suma\"><\/span>\u548c\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>2 \u3064\u306e\u95a2\u6570\u306e\u5408\u8a08\u306e\u5c0e\u95a2\u6570\u306f\u3001\u5404\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u500b\u5225\u306b\u5408\u8a08\u3057\u305f\u3082\u306e\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\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-cec257ea65c3d37da6460f8f1ab6bb1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)+g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)+g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"463\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3064\u307e\u308a\u30012 \u3064\u306e\u95a2\u6570\u3092\u5225\u3005\u306b\u5c0e\u51fa\u3057\u3066\u304b\u3089\u305d\u308c\u3089\u3092\u52a0\u7b97\u3059\u308b\u3053\u3068\u306f\u3001\u6700\u521d\u306b\u95a2\u6570\u3092\u52a0\u7b97\u3057\u3066\u304b\u3089\u5c0e\u95a2\u6570\u3092\u53d6\u5f97\u3059\u308b\u3053\u3068\u3068\u540c\u3058\u3067\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-dune-somme.webp\" alt=\"\u5408\u8a08\u304b\u3089\u5c0e\u304d\u51fa\u3055\u308c\u308b\" class=\"wp-image-2035\" width=\"243\" height=\"243\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u52a0\u7b97\u306e\u5fae\u5206\u898f\u5247\u306f\u6e1b\u7b97\u306b\u3082\u9069\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u95a2\u6570\u306e\u524d\u306b\u6b63\u7b26\u53f7\u3067\u306f\u306a\u304f\u8ca0\u7b26\u53f7\u304c\u3042\u308b\u5834\u5408\u3001\u540c\u3058\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u5fae\u5206\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\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-6a93098fe108be6019d44ba2d0f82108_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)\\pm g(x) \\quad\\color{orange}\\bm{\\longrightarrow}\\quad\\color{black} z'(x)=f'(x)\\pm g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"463\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u3055\u3089\u306b\u3001\u52a0\u7b97\u306f\u7d50\u5408\u7279\u6027\u3092\u6301\u3064\u6f14\u7b97\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u95a2\u6570\u5168\u4f53\u306e\u5c0e\u95a2\u6570\u306f\u5404\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306e\u52a0\u7b97\u3067\u3042\u308a\u7d9a\u3051\u308b\u305f\u3081\u3001\u52a0\u7b97\u306b\u542b\u307e\u308c\u308b\u52a0\u7b97\u306e\u6570\u306f\u91cd\u8981\u3067\u306f\u3042\u308a\u307e\u305b\u3093\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-05ceda7dfbdbac4960b012f62d17c8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}z(x)=f(x)\\pm g(x) \\pm h(x)\\pm \\dots\\\\[1.5ex]\\color{orange}\\bm{\\downarrow}\\quad\\color{black} \\\\[1.5ex]z'(x)=f'(x)\\pm g'(x)\\pm h'(x)\\pm \\dots\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"261\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-derivada-de-una-suma\"><\/span>\u548c\u306e\u5c0e\u95a2\u6570\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u548c\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u3089\u3001\u95a2\u6570\u306e\u548c\u304c\u3069\u306e\u3088\u3046\u306b\u5c0e\u51fa\u3055\u308c\u308b\u304b\u3092\u5b8c\u5168\u306b\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u6f14\u7b97\u306e\u5c0e\u95a2\u6570\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u898b\u3066\u3044\u304d\u307e\u3059\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-derivada-de-una-suma-de-funciones-potenciales\"><\/span>\u4f8b 1: \u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u306e\u548c\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-efca27bad0818b86e6e42ee15a31ed6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=3x^2+5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"125\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>2 \u3064\u306e\u95a2\u6570\u306e\u5408\u8a08\u306e\u5c0e\u95a2\u6570\u306f\u3001\u5404\u95a2\u6570\u3092\u500b\u5225\u306b\u5c0e\u95a2\u6570\u3057\u305f\u3082\u306e\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u521d\u306b\u5404\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u3092\u500b\u5225\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-69\">\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-5e625836da38ce78d816c887fd842fff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ 3x^2=6x\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"95\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\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-f575779fe1f9c29e907e67f622cb5411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ 5x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"76\" 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\u3001\u8a08\u7b97\u3055\u308c\u305f 2 \u3064\u306e\u5c0e\u95a2\u6570\u306e\u5408\u8a08\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-8a8dcfca37df757df3fd79292ead67b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=6x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-derivada-de-una-suma-de-funciones-diferentes\"><\/span>\u4f8b 2: \u3055\u307e\u3056\u307e\u306a\u95a2\u6570\u306e\u5408\u8a08\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-0c94ae34a2f2fe6741b9233bde69c420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{sen}(x)+\\ln(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"166\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u95a2\u6570\u306e\u5408\u8a08\u3092\u5fae\u5206\u3059\u308b\u306b\u306f\u30012 \u3064\u306e\u95a2\u6570\u3092\u500b\u5225\u306b\u5fae\u5206\u3057\u3066\u304b\u3089\u52a0\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u95a2\u6570\u3092\u5c0e\u51fa\u3057\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-72\">\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-e1fd0d9e783b091d26fe14a6f9523801_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx} \\ \\text{sen}(x)=\\text{cos}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"144\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\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-630f2b7757bfc7fbc7fe540313c526b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d}{dx}\\ \\ln (x)=\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"103\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p>\u305d\u3057\u3066\u3001\u898b\u3064\u304b\u3063\u305f 2 \u3064\u306e\u5c0e\u95a2\u6570\u3092\u8ffd\u52a0\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-d74c893fd6ae38b019a934d75b39b921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=\\text{cos}(x)+\\cfrac{1}{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"145\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3-derivada-de-una-suma-al-cuadrado\"><\/span>\u4f8b 3: \u4e8c\u4e57\u548c\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-fc55182666ca330acaf33748f94e1b06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\left(3x^4+7x^2+1\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p>\u3053\u306e\u5834\u5408\u3001\u95a2\u6570\u306e\u5408\u8a08\u3092\u3079\u304d\u4e57\u3057\u305f\u306e\u3067\u3001\u8907\u5408\u95a2\u6570\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9023\u9396\u898f\u5247\u3092\u9069\u7528\u3057\u3066\u95a2\u6570\u5168\u4f53\u3092\u5c0e\u51fa\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-3d5f04a22b460b05368b60eba4a74c4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2\\left(3x^4+7x^2+1\\right)\\cdot (12x^3+14x)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"303\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u53c2\u7167:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ja\/\u96fb\u529b\u30db\u309a\u30c6\u30f3\u30b7\u30e3\u30eb\u95a2\u6570\u306e\u5c0e\u95a2\u6570\/\">\u3079\u304d\u4e57\u306e\u5c0e\u51fa<\/a><\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-derivadas-de-sumas-de-funciones\"><\/span>\u95a2\u6570\u306e\u548c\u306e\u5fae\u5206\u306b\u95a2\u3059\u308b\u6f14\u7fd2\u3092\u89e3\u6c7a\u3057\u307e\u3057\u305f\u3002<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b21\u306e\u95a2\u6570\u306e\u548c\u3092\u5c0e\u51fa\u3057\u307e\u3059<\/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-ae19a6909252c6385e64b78c67688db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f(x)=6x^3+9x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"159\" 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-d7239b728b0ae9ef7f14e34910f71c8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f(x)=x^4+10x^3+5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" 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-d421d72da5a4af38dda14af4151fba4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f(x)=3x^2-4x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"182\" 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-2df5e88a0c25ffd19b52aa2c950a1c1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f(x)=\\text{cos}(x)+e^{3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"177\" 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-3f844607b5234ee8282802ef2ad19dac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f(x)=\\left(x^3+4x^2+6x\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"213\" 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-202ed150e3c26b6b56de412d7f8a5884_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f(x)=\\log_3(8x^2+2x)-x^7+e^{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"277\" style=\"vertical-align: -5px;\"><\/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-c5e6d4e0f405a797739dba71003c60ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A) } f'(x)=18x^2+18x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"174\" 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-1069a5e43f43a569cfb3db5f8d9b7331_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B) } f'(x)=4x^3+30x^2+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-93b4f2f1938846ce64f102e4964cbbef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C) } f'(x)=6x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" 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-190b6cc92e8c9a9119d0255247b7e14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D) } f'(x)=-\\text{sen}(x)+3e^{3x}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"205\" 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-fa0eabdbceafaf3e9b7535da9d1d520a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E) } f'(x)=3\\left(x^3+4x^2+6x\\right)^2\\cdot (3x^2+8x+6)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"354\" 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-40fc02db80aa8a889f70ca9f25d295c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F) } f'(x)=\\cfrac{16x+2}{(8x^2+2x)\\ln(3)}-7x^6+2x\\cdot e^{x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"334\" style=\"vertical-align: -17px;\"><\/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-una-suma\"><\/span>\u5408\u8a08\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>\u3053\u306e\u6700\u5f8c\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u95a2\u6570\u306e\u548c\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u3053\u308c\u3092\u884c\u3046\u305f\u3081\u306b\u3001\u6b21\u306e\u3088\u3046\u306a\u5c0e\u95a2\u6570\u306e\u6570\u5b66\u7684\u5b9a\u7fa9\u306b\u983c\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-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>\u6b21\u306b\u3001z \u3092 2 \u3064\u306e\u7570\u306a\u308b\u95a2\u6570\u306e\u5408\u8a08\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-4d2d91569fa3b33d834dead8ca02ff3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"z(x)=f(x)+g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" 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-17f0dc216847872551637f676d1ff0b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{z(x+h)-z(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"215\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u3053\u3053\u3067\u3001\u6975\u9650\u5f0f\u306e\u95a2\u6570\u306e\u5408\u8a08\u3092 z \u306b\u7f6e\u304d\u63db\u3048\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-feab6b99cc6e3bfad015b988f16c5241_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{\\bigl[f(x+h)+g(x+h)\\bigr]-\\bigl[f(x)+g(x)\\bigr]}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"389\" 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-73d3c0e1781a7ec65721ab6aef3d840a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)+g(x+h)-f(x)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"359\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u5206\u6570\u3092\u3001\u305d\u308c\u305e\u308c\u306e\u52a0\u7b97\u95a2\u6570\u306b\u5bfe\u5fdc\u3059\u308b 2 \u3064\u306e\u5206\u6570\u306e\u548c\u306b\u306a\u308b\u3088\u3046\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-e7b00aae0064e00a5e8a2f57e54fa339_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\left[\\frac{f(x+h)-f(x)}{h}+\\frac{g(x+h)-g(x)}{h}\\right]\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"379\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u5236\u9650\u306e\u7279\u6027\u306e\u304a\u304b\u3052\u3067\u3001\u5408\u8a08\u306e\u5236\u9650\u306f\u5236\u9650\u306e\u5408\u8a08\u3068\u540c\u7b49\u3067\u3042\u308b\u305f\u3081\u3001\u524d\u306e\u5f0f\u3092 2 \u3064\u306e\u5236\u9650\u306b\u5206\u3051\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-6c8091e8c717504ae86efff94b5d8e3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=\\lim_{h \\to 0}\\frac{f(x+h)-f(x)}{h}+\\lim_{h \\to 0}\\frac{g(x+h)-g(x)}{h}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"394\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p>\u305d\u3057\u3066\u3001\u4e0a\u8a18\u306e\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u3067\u898b\u305f\u3088\u3046\u306b\u3001\u5404\u6975\u9650\u306f\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u7b49\u4fa1\u6027\u304c\u9054\u6210\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-cea8c29e93381736297a8f6aa46c83fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle z'(x)=f'(x)+g'(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"158\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\u95a2\u6570\u306e\u548c\uff08\u516c\u5f0f\uff09\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u548c\u306e\u5fae\u5206\u306e\u4f8b\u3092\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u548c\u306e\u5fae\u5206\u306e\u6f14\u7fd2\u3092\u89e3\u3044\u3066\u7df4\u7fd2\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u5408\u8a08\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f\u306e\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u793a\u3057\u307e\u3059\u3002 \u548c\u306e\u5c0e\u95a2\u6570\u306e\u516c\u5f0f 2 \u3064 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e5%92%8c%e3%81%ae%e5%b0%8e%e9%96%a2%e6%95%b0\/\"> <span class=\"screen-reader-text\">\u5408\u8a08\u304b\u3089\u5c0e\u51fa<\/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-33","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized 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