{"id":4815,"date":"2020-12-03T17:26:10","date_gmt":"2020-12-03T08:26:10","guid":{"rendered":"https:\/\/www.educational-lounge.com\/?p=4815"},"modified":"2020-12-03T23:51:56","modified_gmt":"2020-12-03T14:51:56","slug":"%e6%95%b0%e5%ad%a6%e2%85%b2%e3%81%ae%e5%be%ae%e7%a9%8d%e5%88%86%e5%9f%ba%e6%9c%ac%e5%85%ac%e5%bc%8f%e9%9b%86","status":"publish","type":"post","link":"https:\/\/www.educational-lounge.com\/?p=4815","title":{"rendered":"\u6570\u5b66\u2162\u306e\u5fae\u7a4d\u5206\u57fa\u672c\u516c\u5f0f\u96c6"},"content":{"rendered":"<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.5\/MathJax.js?config=TeX-AMS_CHTML\" type=\"text\/javascript\">    \n    MathJax.Hub.Config({\n        HTML: [\"input\/TeX\",\"output\/HTML-CSS\"],\n        TeX: {\n               Macros: {\n                        bm: [\"\\\\boldsymbol{#1}\", 1]},\n               extensions: [\"AMSmath.js\",\"AMSsymbols.js\",\"color.js\"],\n               equationNumbers: { autoNumber: \"AMS\" } },\n        extensions: [\"tex2jax.js\"],\n        jax: [\"input\/TeX\",\"output\/HTML-CSS\"],\n        tex2jax: { inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n                   displayMath: [ ['$$','$$']], \n                   processEscapes: true },\n        \"HTML-CSS\": { availableFonts: [\"TeX\"],\n                      linebreaks: { automatic: true } }\n    });\n<\/script>\u3069\u3046\u3082\u3001\u3053\u3093\u306b\u3061\u306f\u3002\u9ad8\u6a4b\u4f73\u4f51\u3067\u3059\u3002<br \/>\n\u4eca\u56de\u306f\u6570\u5b66\u2162\u306e\u5358\u5143\u300c\u5fae\u5206\u7a4d\u5206\u300d\u306e\u57fa\u672c\u516c\u5f0f\u3092\u7d39\u4ecb\u3044\u305f\u3057\u307e\u3059\u3002<\/p>\n<h2 style=\"padding: .25em 0.5em .75em; border-left: 6px solid #3300ff; border-bottom: 1px solid #ccc;\">\u5fae\u5206\u306e\u57fa\u672c\u516c\u5f0f<\/h2>\n<ol>\n<li>$f(x)=x^\\alpha$\uff08$\\alpha$\u306f\u5b9f\u6570\uff09\u306e\u5fae\u5206\u306f$f'(x)=\\alpha x^{\\alpha-1}$<\/li>\n<li>$f(x)=\\sqrt{x}$\u306e\u5fae\u5206\u306f$f'(x)=\\frac{1}{2\\sqrt{x}}$<\/li>\n<li>$f(x)=\\frac{1}{x}$\u306e\u5fae\u5206\u306f$f'(x)=-\\frac{1}{x^2}$<\/li>\n<li>$f(x)=\\sin x$\u306e\u5fae\u5206\u306f$f'(x)=\\cos x$<\/li>\n<li>$f(x)=\\cos x$\u306e\u5fae\u5206\u306f$f'(x)=-\\sin x$<\/li>\n<li>$f(x)=\\tan x$\u306e\u5fae\u5206\u306f$f'(x)=\\frac{1}{\\cos^2 x}$<\/li>\n<li>$f(x)=e^x$\u306e\u5fae\u5206\u306f$f'(x)=e^x$<\/li>\n<li>$f(x)=a^x (a&gt;0, a\\neq 1)$\u306e\u5fae\u5206\u306f$f'(x)=a^x \\log a$<\/li>\n<li>$f(x)=\\log |x|$\u306e\u5fae\u5206\u306f$f'(x)=\\frac{1}{x}$<\/li>\n<\/ol>\n<p>\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u983b\u7e41\u306b\u5fae\u5206\u3059\u308b\u306e\u3067\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2 style=\"padding: .25em 0.5em .75em; border-left: 6px solid #3300ff; border-bottom: 1px solid #ccc;\">\u7a4d\u5206\u306e\u57fa\u672c\u516c\u5f0f<\/h2>\n<p>$C$\u3092\u7a4d\u5206\u5b9a\u6570\u3068\u3059\u308b\u3002<\/p>\n<ol>\n<li>$\\int x^\\alpha dx=\\frac{1}{\\alpha\\,+1}x^{\\alpha +1}+C$\uff08$\\alpha$\u306f$-1$\u4ee5\u5916\u306e\u5b9f\u6570\uff09<\/li>\n<li>$\\int \\frac{1}{x}dx=\\log |x|+C$<\/li>\n<li>$\\int \\frac{1}{x^2}dx=-\\frac{1}{x}+C$<\/li>\n<li>$\\int \\cos x\\,dx=\\sin x+C$<\/li>\n<li>$\\int \\sin x\\,dx=-\\cos x+C$<\/li>\n<li>$\\int \\frac{1}{\\cos^2 x}dx=\\tan x+C$<\/li>\n<li>$\\int \\frac{1}{\\sin^2 x}dx=-\\frac{1}{\\tan x}+C$<\/li>\n<li>$\\int e^x \\,dx=e^x +C$<\/li>\n<li>$\\int a^x \\,dx=\\frac{a^x}{\\log a}+C(a&gt;0,a\\neq 1)$<\/li>\n<li>$\\int \\log x\\,dx=x\\log x-x+C$<\/li>\n<\/ol>\n<p>7.\u306f\u5fae\u5206\u306e\u516c\u5f0f\u306b\u5165\u308c\u3066\u3044\u307e\u305b\u3093\u304c\u3001\u7a4d\u5206\u3067\u306f\u77e5\u8b58\u3068\u3057\u3066\u899a\u3048\u3066\u3044\u304f\u3068\u3088\u3044\u3067\u3057\u3087\u3046\u3002<br \/>\n\u3082\u3061\u308d\u3093\u3001$\\frac{1}{\\tan x}$\u3092\u5fae\u5206\u3059\u308b\u3068\u3001$-\\frac{1}{\\sin^2 x}$\u3068\u306a\u308b\u3053\u3068\u304b\u3089\u7c21\u5358\u306b\u78ba\u304b\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u300110.\u306f\u90e8\u5206\u7a4d\u5206\u3068\u3044\u3046\u65b9\u6cd5\u3092\u4f7f\u3044\u307e\u3059\u304c\u3001$\\log$\u306e\u3064\u304f\u95a2\u6570\u3092\u7a4d\u5206\u3059\u308b\u6a5f\u4f1a\u306f\u591a\u3044\u306e\u3067\u3001\u516c\u5f0f\u3068\u3057\u3066\u899a\u3048\u308b\u3053\u3068\u3092\u304a\u3059\u3059\u3081\u3057\u307e\u3059\u3002<\/p>\n<h2 style=\"padding: .25em 0.5em .75em; border-left: 6px solid #3300ff; border-bottom: 1px solid #ccc;\">\u304a\u308f\u308a\u306b<\/h2>\n<p>\u3053\u3053\u3067\u7d39\u4ecb\u3057\u305f\u3082\u306e\u306f\u57fa\u672c\u516c\u5f0f\u3067\u3059\u3002<br \/>\n\u4ed6\u306b\u3082\u7a4d\u306e\u5fae\u5206\u3001\u5546\u306e\u5fae\u5206\u3001\u90e8\u5206\u7a4d\u5206\u3001\u7f6e\u63db\u7a4d\u5206\u306a\u3069\u307e\u3060\u307e\u3060\u5b66\u7fd2\u3059\u3079\u304d\u3053\u3068\u306f\u3044\u3063\u3071\u3044\u3042\u308a\u307e\u3059\u3002<br \/>\n\u3053\u308c\u3089\u306e\u57fa\u672c\u516c\u5f0f\u3092\u304a\u3055\u3048\u305f\u4e0a\u3067\u30b9\u30c6\u30c3\u30d7\u30a2\u30c3\u30d7\u3057\u3066\u3044\u3063\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4eca\u56de\u306f\u3053\u306e\u8fba\u3067\uff01<\/p>\n\n","protected":false},"excerpt":{"rendered":"<p>\u3069\u3046\u3082\u3001\u3053\u3093\u306b\u3061\u306f\u3002\u9ad8\u6a4b\u4f73\u4f51\u3067\u3059\u3002 \u4eca\u56de\u306f\u6570\u5b66\u2162\u306e\u5358\u5143\u300c\u5fae\u5206\u7a4d\u5206\u300d\u306e\u57fa\u672c\u516c\u5f0f\u3092\u7d39\u4ecb\u3044\u305f\u3057\u307e\u3059\u3002 \u5fae\u5206\u306e\u57fa\u672c\u516c\u5f0f $f(x)=x^\\alpha$\uff08$\\alpha$\u306f\u5b9f\u6570\uff09\u306e\u5fae\u5206\u306f$f'(x)=\\alpha x^{\\alph\u2026<\/p>\n","protected":false},"author":25,"featured_media":4357,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,146,5],"tags":[],"class_list":["post-4815","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-6","category-146","category-5"],"_links":{"self":[{"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=\/wp\/v2\/posts\/4815","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=\/wp\/v2\/users\/25"}],"replies":[{"embeddable":true,"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4815"}],"version-history":[{"count":17,"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=\/wp\/v2\/posts\/4815\/revisions"}],"predecessor-version":[{"id":4836,"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=\/wp\/v2\/posts\/4815\/revisions\/4836"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=\/wp\/v2\/media\/4357"}],"wp:attachment":[{"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.educational-lounge.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}