(\partial)/(\partial u)(sqrt(v/u))

解

\frac{\partial}{\partial u} (\frac{v}{u})

- \frac{v}{2 u ^{\frac{3}{2}}}

解答ステップ

\frac{\partial}{\partial u} (\frac{v}{u})

v

を定数として扱う

連鎖法則を適用:

\frac{1}{2 \frac{v}{u}} \frac{\partial}{\partial u} (\frac{v}{u})

= \frac{1}{2 \frac{v}{u}} \frac{\partial}{\partial u} (\frac{v}{u})

\frac{\partial}{\partial u} (\frac{v}{u}) = - \frac{v}{u ^{2}}

= \frac{1}{2 \frac{v}{u}} (- \frac{v}{u ^{2}})

簡素化

\frac{1}{2 \frac{v}{u}} (- \frac{v}{u ^{2}}) : - \frac{v}{2 u ^{\frac{3}{2}}}

= - \frac{v}{2 u ^{\frac{3}{2}}}