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

The answer to (\partial)/(\partial u)(sqrt(u^5+v^9)) is (5u^4)/(2sqrt(u^5+v^9))

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

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

\frac{5 u ^{4}}{2 u ^{5} + v ^{9}}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial u} (u^{5} + v^{9}) = 5 u^{4}

= \frac{1}{2 u ^{5} + v ^{9}} \cdot 5 u^{4}

Simplify

\frac{1}{2 u ^{5} + v ^{9}} \cdot 5 u^{4} : \frac{5 u ^{4}}{2 u ^{5} + v ^{9}}

= \frac{5 u ^{4}}{2 u ^{5} + v ^{9}}

\int_{1}^{e^{4}} \frac{ln ^{3} ( x ^{2} )}{x} d x

\frac{d}{d x} (x^{\frac{4}{3}} + 4 x^{\frac{1}{3}})

\frac{\partial}{\partial x} (sin (x^{4} + y^{3}))

f (x) = x^{2} - 3, (4, 13)

x \to 0 + lim (\frac{7}{x} - \frac{7}{∣ x ∣})

What is (\partial)/(\partial u)(sqrt(u^5+v^9)) ?
The answer to (\partial)/(\partial u)(sqrt(u^5+v^9)) is (5u^4)/(2sqrt(u^5+v^9))