What is (\partial)/(\partial u)(tan(u/v)) ?

The answer to (\partial)/(\partial u)(tan(u/v)) is (sec^2(u/v))/v

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

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

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

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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}

Simplify

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

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

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What is (\partial)/(\partial u)(tan(u/v)) ?
The answer to (\partial)/(\partial u)(tan(u/v)) is (sec^2(u/v))/v