(\partial)/(\partial x)(sqrt((18)/(xy)))

解

\frac{\partial}{\partial x} (\frac{18}{x y})

- \frac{3}{2 x ^{\frac{3}{2}} y}

解答ステップ

\frac{\partial}{\partial x} (\frac{18}{x y})

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 \frac{18}{x y}} \frac{\partial}{\partial x} (\frac{18}{x y})

= \frac{1}{2 \frac{18}{x y}} \frac{\partial}{\partial x} (\frac{18}{x y})

\frac{\partial}{\partial x} (\frac{18}{x y}) = - \frac{18}{y x ^{2}}

= \frac{1}{2 \frac{18}{x y}} (- \frac{18}{y x ^{2}})

簡素化

\frac{1}{2 \frac{18}{x y}} (- \frac{18}{y x ^{2}}) : - \frac{3}{2 x ^{\frac{3}{2}} y}

= - \frac{3}{2 x ^{\frac{3}{2}} y}