What is (\partial)/(\partial u)(sqrt(u^9+v^5)) ?

The answer to (\partial)/(\partial u)(sqrt(u^9+v^5)) is (9u^8)/(2sqrt(u^9+v^5))

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(\partial)/(\partial u)(sqrt(u^9+v^5))

\frac{\partial}{\partial u} (u^{9} + v^{5})

\frac{9 u ^{8}}{2 u ^{9} + v ^{5}}

Solution steps

\frac{\partial}{\partial u} (u^{9} + v^{5})

Treat

v

as a constant

Apply the chain rule:

\frac{1}{2 u ^{9} + v ^{5}} \frac{\partial}{\partial u} (u^{9} + v^{5})

= \frac{1}{2 u ^{9} + v ^{5}} \frac{\partial}{\partial u} (u^{9} + v^{5})

\frac{\partial}{\partial u} (u^{9} + v^{5}) = 9 u^{8}

= \frac{1}{2 u ^{9} + v ^{5}} \cdot 9 u^{8}

Simplify

\frac{1}{2 u ^{9} + v ^{5}} \cdot 9 u^{8} : \frac{9 u ^{8}}{2 u ^{9} + v ^{5}}

= \frac{9 u ^{8}}{2 u ^{9} + v ^{5}}

What is (\partial)/(\partial u)(sqrt(u^9+v^5)) ?
The answer to (\partial)/(\partial u)(sqrt(u^9+v^5)) is (9u^8)/(2sqrt(u^9+v^5))