(\partial)/(\partial x)(x^{0.7}y^{0.3})

解

\frac{\partial}{\partial x} (x^{0.7} y^{0.3})

\frac{0.7 y ^{0.3}}{x ^{0.3}}

解答ステップ

\frac{\partial}{\partial x} (x^{0.7} y^{0.3})

y

を定数として扱う

定数を除去:

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

= y^{0.3} \frac{\partial}{\partial x} (x^{0.7})

乗の法則を適用:

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

= y^{0.3} \cdot 0.7 x^{0.7 - 1}

簡素化

y^{0.3} \cdot 0.7 x^{0.7 - 1} : \frac{0.7 y ^{0.3}}{x ^{0.3}}

= \frac{0.7 y ^{0.3}}{x ^{0.3}}