(\partial)/(\partial x)(10x^{1/4}*2y^{3/4})

解

\frac{\partial}{\partial x} (10 x^{\frac{1}{4}} \cdot 2 y^{\frac{3}{4}})

\frac{5 y ^{\frac{3}{4}}}{x ^{\frac{3}{4}}}

解答ステップ

\frac{\partial}{\partial x} (10 x^{\frac{1}{4}} \cdot 2 y^{\frac{3}{4}})

簡素化

10 x^{\frac{1}{4}} \cdot 2 y^{\frac{3}{4}} : 20 x^{\frac{1}{4}} y^{\frac{3}{4}}

= \frac{\partial}{\partial x} (20 x^{\frac{1}{4}} y^{\frac{3}{4}})

y

を定数として扱う

定数を除去:

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

= 20 y^{\frac{3}{4}} \frac{\partial}{\partial x} (x^{\frac{1}{4}})

乗の法則を適用:

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

= 20 y^{\frac{3}{4}} \frac{1}{4} x^{\frac{1}{4} - 1}

簡素化

20 y^{\frac{3}{4}} \frac{1}{4} x^{\frac{1}{4} - 1} : \frac{5 y ^{\frac{3}{4}}}{x ^{\frac{3}{4}}}

= \frac{5 y ^{\frac{3}{4}}}{x ^{\frac{3}{4}}}