(\partial)/(\partial x)(25x^{(3/4)}y^{1/4})

解

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})

\frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

解答ステップ

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})

y

を定数として扱う

定数を除去:

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

= 25 y^{\frac{1}{4}} \frac{\partial}{\partial x} (x^{\frac{3}{4}})

乗の法則を適用:

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

= 25 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1}

簡素化

25 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1} : \frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

= \frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}