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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 Constant factor rule in differentiation ： ウィキペディア英語版 Constant factor rule in differentiation In calculus, the constant factor rule in differentiation, also known as The Kutz Rule , allows one to take constants outside a derivative and concentrate on differentiating the function of x itself. This is a part of the linearity of differentiation. Consider a differentiable function :$g(x)\; =\; k\; \backslash cdot\; f(x).$ where ''k'' is a constant. Use the formula for differentiation from first principles to obtain: :$g\text{'}(x)\; =\; \backslash lim\_\; \backslash frac$ :$g\text{'}(x)\; =\; \backslash lim\_\; \backslash frac$ :$g\text{'}(x)\; =\; \backslash lim\_\; \backslash frac$ :$g\text{'}(x)\; =\; k\; \backslash lim\_\; \backslash frac$ :$g\text{'}(x)\; =\; k\; \backslash cdot\; f\text{'}(x).$ This is the statement of the constant factor rule in differentiation, in Lagrange's notation for differentiation. In Leibniz's notation, this reads :$\backslash frac\; =\; k\; \backslash cdot\; \backslash frac.$ If we put ''k''=-1 in the constant factor rule for differentiation, we have: :$\backslash frac\; =\; -\backslash frac.$ ==Comment on proof== Note that for this statement to be true, ''k'' must be a constant, or else the ''k'' can't be taken outside the limit in the line marked ( *). If ''k'' depends on ''x'', there is no reason to think ''k(x+h)'' = ''k(x)''. In that case the more complicated proof of the product rule applies. 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「Constant factor rule in differentiation」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.