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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 Leibnitz rule ： ウィキペディア英語版 Product rule In calculus, the product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as :$(f\backslash cdot\; g)\text{'}=f\text{'}\backslash cdot\; g+f\backslash cdot\; g\text{'}\; \backslash ,\backslash !$ or in the Leibniz notation :$\backslash dfrac(u\backslash cdot\; v)=u\backslash cdot\; \backslash dfrac+v\backslash cdot\; \backslash dfrac$. In differentials notation, this can be written as :$d(uv)=u\backslash ,dv+v\backslash ,du$. In Leibniz notation, the derivative of the product of three functions (not to be confused with Euler's triple product rule) is :$\backslash dfrac(u\backslash cdot\; v\; \backslash cdot\; w)=\backslash dfrac\; \backslash cdot\; v\; \backslash cdot\; w\; +\; u\; \backslash cdot\; \backslash dfrac\; \backslash cdot\; w\; +\; u\backslash cdot\; v\backslash cdot\; \backslash dfrac$. == Discovery == Discovery of this rule is credited to Gottfried Leibniz, who demonstrated it using differentials. (However, Child (2008) argues that it is due to Isaac Barrow). Here is Leibniz's argument: Let ''u''(''x'') and ''v''(''x'') be two differentiable functions of ''x''. Then the differential of ''uv'' is : $$ \begin d(u\cdot v) & Since the term ''du''·''dv'' is "negligible" (compared to ''du'' and ''dv''), Leibniz concluded that :$d(u\backslash cdot\; v)\; =\; v\backslash cdot\; du\; +\; u\backslash cdot\; dv\; \backslash ,\backslash !$ and this is indeed the differential form of the product rule. If we divide through by the differential ''dx'', we obtain :$\backslash frac\; (u\backslash cdot\; v)\; =\; v\; \backslash cdot\; \backslash frac\; +\; u\; \backslash cdot\; \backslash frac\; \backslash ,\backslash !$ which can also be written in Lagrange's notation as :$(u\backslash cdot\; v)\text{'}\; =\; v\backslash cdot\; u\text{'}\; +\; u\backslash cdot\; v\text{'}.\; \backslash ,\backslash !$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Product 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.