(\partial)/(\partial x)(100x^{0.66}y^{0.34})

解

\frac{\partial}{\partial x} (100 x^{0.66} y^{0.34})

\frac{66 y ^{0.34}}{x ^{0.34}}

解答ステップ

\frac{\partial}{\partial x} (100 x^{0.66} y^{0.34})

y

を定数として扱う

定数を除去:

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

= 100 y^{0.34} \frac{\partial}{\partial x} (x^{0.66})

乗の法則を適用:

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

= 100 y^{0.34} \cdot 0.66 x^{0.66 - 1}

簡素化

100 y^{0.34} \cdot 0.66 x^{0.66 - 1} : \frac{66 y ^{0.34}}{x ^{0.34}}

= \frac{66 y ^{0.34}}{x ^{0.34}}