(\partial}{\partial L}(L^{1/4)/K ^{1/4})

解

\frac{\partial}{\partial L} (L^{\frac{1}{4}} K^{\frac{1}{4}})

\frac{K ^{\frac{1}{4}}}{4 L ^{\frac{3}{4}}}

解答ステップ

\frac{\partial}{\partial L} (L^{\frac{1}{4}} K^{\frac{1}{4}})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= K^{\frac{1}{4}} \frac{\partial}{\partial L} (L^{\frac{1}{4}})

乗の法則を適用:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= K^{\frac{1}{4}} \frac{1}{4} L^{\frac{1}{4} - 1}

簡素化

K^{\frac{1}{4}} \frac{1}{4} L^{\frac{1}{4} - 1} : \frac{K ^{\frac{1}{4}}}{4 L ^{\frac{3}{4}}}

= \frac{K ^{\frac{1}{4}}}{4 L ^{\frac{3}{4}}}