(\partial)/(\partial x)((x-5)^{1/4}y^{1/4})

解

\frac{\partial}{\partial x} ((x - 5)^{\frac{1}{4}} y^{\frac{1}{4}})

\frac{y ^{\frac{1}{4}}}{4 ( x - 5 ) ^{\frac{3}{4}}}

解答ステップ

\frac{\partial}{\partial x} ((x - 5)^{\frac{1}{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^{'}

= y^{\frac{1}{4}} \frac{\partial}{\partial x} ((x - 5)^{\frac{1}{4}})

連鎖法則を適用:

\frac{1}{4 ( x - 5 ) ^{\frac{3}{4}}} \frac{\partial}{\partial x} (x - 5)

= \frac{1}{4 ( x - 5 ) ^{\frac{3}{4}}} \frac{\partial}{\partial x} (x - 5)

\frac{\partial}{\partial x} (x - 5) = 1

= y^{\frac{1}{4}} \frac{1}{4 ( x - 5 ) ^{\frac{3}{4}}} \cdot 1

簡素化

y^{\frac{1}{4}} \frac{1}{4 ( x - 5 ) ^{\frac{3}{4}}} \cdot 1 : \frac{y ^{\frac{1}{4}}}{4 ( x - 5 ) ^{\frac{3}{4}}}

= \frac{y ^{\frac{1}{4}}}{4 ( x - 5 ) ^{\frac{3}{4}}}