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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 Leibniz rule (generalized product rule) ： ウィキペディア英語版 General Leibniz rule In calculus, the general Leibniz rule,〔Olver, Applications of Lie groups to differential equations, page 318〕 named after Gottfried Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if ''u'' and ''v'' are ''n''-times differentiable functions, then product ''uv'' is also ''n''-times differentiable and its ''n''th derivative is given by :$(uv)^=\backslash sum\_^n\; u^\; v^$ where $=$ is the binomial coefficient. This can be proved by using the product rule and mathematical induction. ==More than two factors== The formula can be generalized to the product of ''m'' differentiable functions ''f''1,...,''f''''m''. :$\backslash left(f\_1\; f\_2\; \backslash cdots\; f\_m\backslash right)^=\backslash sum\_$ \prod_f_^\,, where the sum extends over all ''m''-tuples (''k''1,...,''k''''m'') of non-negative integers with $\backslash sum\_^m\; k\_t=n$ and :$$ = \frac are the multinomial coefficients. This is akin to the multinomial formula from algebra. 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「General Leibniz 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.