{"id":4198,"date":"2013-12-10T12:00:03","date_gmt":"2013-12-10T03:00:03","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4198"},"modified":"2014-09-10T16:52:25","modified_gmt":"2014-09-10T07:52:25","slug":"post-4198","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4198","title":{"rendered":"\u5fae\u5206"},"content":{"rendered":"

\u5fae\u5206<\/h3>\n

\u3000\u95a2\u6570 y = f(x) \u306e\u3042\u308b\u70b9\u3067\u306e\u5fae\u5206\u4fc2\u6570\u306f\u4e0b\u8a18\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n

\\displaystyle f'(x) = \\lim\\limits_{h \\rightarrow 0}\\frac{f(x+h) - f(x)}{h} = \\lim\\limits_{\\Delta x \\rightarrow 0}\\frac{\\Delta y}{\\Delta x} = \\frac{dy}{dx}<\/p>\n

\u5fae\u5206\u516c\u5f0f<\/h3>\n

\u3000u, v \u304c x \u306e\u95a2\u6570\u3067\u3042\u308a a, c, p \u304c\u5b9a\u6570\u3092\u793a\u3059\u6642\uff0c\u4ee5\u4e0b\u306e\u5fae\u5206\u516c\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff0e<\/p>\n

\\displaystyle \\frac{d}{dx}(u \\pm v) = \\frac{du}{dx} \\pm \\frac{dv}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}(cu) = c\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}(uv) = u\\frac{dv}{dx} + v\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\left(\\frac{u}{v}\\right) = \\frac{v(du\/dx) - u(dv\/dx)}{v^2}\\\\\\vspace{0.2 in} \\frac{d}{dx}u^p = pu^{p-1}\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}(a^u) = a^u\\ln{a}\\\\\\vspace{0.2 in} \\frac{d}{dx}e^u = e^u\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\ln{u} = \\frac{1}{u}\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\sin{u} = \\cos{u}\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\cos{u} = -\\sin{u}\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\tan{u} = \\sec^2{u}\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\sin^{-1}u = \\frac{1}{\\sqrt{1 - u^2}}\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\cos^{-1}u = \\frac{-1}{\\sqrt{1 - u^2}}\\frac{du}{dx}\\\\\\vspace{0.2 in} \\frac{d}{dx}\\tan^{-1}u = \\frac{1}{\\sqrt{1 + u^2}}\\frac{du}{dx}
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