(\partial)/(\partial u)(tan(u/v))

解

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

\frac{sec ^{2} ( \frac{u}{v} )}{v}

解答ステップ

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

v

を定数として扱う

連鎖法則を適用:

sec^{2} (\frac{u}{v}) \frac{\partial}{\partial u} (\frac{u}{v})

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

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

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

簡素化

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

= \frac{sec ^{2} ( \frac{u}{v} )}{v}