What is (\partial)/(\partial u)(sqrt(u^9+v^7)) ?

The answer to (\partial)/(\partial u)(sqrt(u^9+v^7)) is (9u^8)/(2sqrt(u^9+v^7))

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(\partial)/(\partial u)(sqrt(u^9+v^7))

\frac{\partial}{\partial u} (u^{9} + v^{7})

\frac{9 u ^{8}}{2 u ^{9} + v ^{7}}

Solution steps

\frac{\partial}{\partial u} (u^{9} + v^{7})

Treat

v

as a constant

Apply the chain rule:

\frac{1}{2 u ^{9} + v ^{7}} \frac{\partial}{\partial u} (u^{9} + v^{7})

= \frac{1}{2 u ^{9} + v ^{7}} \frac{\partial}{\partial u} (u^{9} + v^{7})

\frac{\partial}{\partial u} (u^{9} + v^{7}) = 9 u^{8}

= \frac{1}{2 u ^{9} + v ^{7}} \cdot 9 u^{8}

Simplify

\frac{1}{2 u ^{9} + v ^{7}} \cdot 9 u^{8} : \frac{9 u ^{8}}{2 u ^{9} + v ^{7}}

= \frac{9 u ^{8}}{2 u ^{9} + v ^{7}}

\int (cos (x))^{- 1} d x

\frac{d}{d x} (x^{\frac{1}{2}} (3 x^{2} - 35 x + 90))

\int \frac{1}{( 1 + x ) ^{2}} d x

\frac{d}{d x} (5^{5})

What is (\partial)/(\partial u)(sqrt(u^9+v^7)) ?
The answer to (\partial)/(\partial u)(sqrt(u^9+v^7)) is (9u^8)/(2sqrt(u^9+v^7))