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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク quotient rule ： ウィキペディア英語版 quotient rule In calculus, the quotient rule is a method of finding the derivative of a function that is the quotient of two other functions for which derivatives exist. If the function one wishes to differentiate, $f(x)$, can be written as :$f(x)\; =\; \backslash frac$ and $h(x)\backslash not=0$, then the rule states that the derivative of $g(x)/h(x)$ is :$f\text{'}(x)\; =\; \backslash frac.$ More precisely, if all ''x'' in some open set containing the number ''a'' satisfy $h(a)\backslash not=0$, and $g\text{'}(a)$ and $h\text{'}(a)$ both exist, then $f\text{'}(a)$ exists as well and :$f\text{'}(a)=\backslash frac.$ And this can be extended to calculate the second derivative as well (one can prove this by taking the derivative of $f(x)=g(x)(h(x))^$ twice). The result of this is: :$f\text{'}\text{'}(x)=\backslash frac.$ The quotient rule formula can be derived from the product rule and chain rule. == Examples == The derivative of $(4x\; -\; 2)/(x^2\; +\; 1)$ is: : ■ウィキペディアで「quotient rule」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.