(\partial)/(\partial x)(x^{0.25}y^{0.5})

解

\frac{\partial}{\partial x} (x^{0.25} y^{0.5})

\frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

解答ステップ

\frac{\partial}{\partial x} (x^{0.25} y^{0.5})

y

を定数として扱う

定数を除去:

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

= y^{0.5} \frac{\partial}{\partial x} (x^{0.25})

乗の法則を適用:

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

= y^{0.5} \cdot 0.25 x^{0.25 - 1}

簡素化

y^{\frac{1}{2}} \cdot 0.25 x^{0.25 - 1} : \frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

= \frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}