What is (\partial)/(\partial u)(tan(5uv^5)) ?

The answer to (\partial)/(\partial u)(tan(5uv^5)) is sec^2(5uv^5)*5v^5

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(\partial)/(\partial u)(tan(5uv^5))

\frac{\partial}{\partial u} (tan (5 u v^{5}))

sec^{2} (5 u v^{5}) \cdot 5 v^{5}

Solution steps

\frac{\partial}{\partial u} (tan (5 u v^{5}))

Treat

v

as a constant

Apply the chain rule:

sec^{2} (5 u v^{5}) \frac{\partial}{\partial u} (5 u v^{5})

= sec^{2} (5 u v^{5}) \frac{\partial}{\partial u} (5 u v^{5})

\frac{\partial}{\partial u} (5 u v^{5}) = 5 v^{5}

= sec^{2} (5 u v^{5}) \cdot 5 v^{5}

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What is (\partial)/(\partial u)(tan(5uv^5)) ?
The answer to (\partial)/(\partial u)(tan(5uv^5)) is sec^2(5uv^5)*5v^5