What is (\partial)/(\partial u)(sqrt(u^5+v^7)) ?

The answer to (\partial)/(\partial u)(sqrt(u^5+v^7)) is (5u^4)/(2sqrt(u^5+v^7))

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(\partial)/(\partial u)(sqrt(u^5+v^7))

\frac{\partial}{\partial u} (u^{5} + v^{7})

\frac{5 u ^{4}}{2 u ^{5} + v ^{7}}

Solution steps

\frac{\partial}{\partial u} (u^{5} + v^{7})

Treat

v

as a constant

Apply the chain rule:

\frac{1}{2 u ^{5} + v ^{7}} \frac{\partial}{\partial u} (u^{5} + v^{7})

= \frac{1}{2 u ^{5} + v ^{7}} \frac{\partial}{\partial u} (u^{5} + v^{7})

\frac{\partial}{\partial u} (u^{5} + v^{7}) = 5 u^{4}

= \frac{1}{2 u ^{5} + v ^{7}} \cdot 5 u^{4}

Simplify

\frac{1}{2 u ^{5} + v ^{7}} \cdot 5 u^{4} : \frac{5 u ^{4}}{2 u ^{5} + v ^{7}}

= \frac{5 u ^{4}}{2 u ^{5} + v ^{7}}

\frac{\partial}{\partial x} (y^{2} + 16)

\frac{d}{d x} (\frac{x + 1}{x + 5})

y^{^{''}} - 8 y^{^{'}} + 25 y = 208 sin (3 x)

y^{^{'}} = \frac{2 x y}{x ^{2} - y ^{2}}

4 x = 4 y - y^{2}, 4 x - y = 0

What is (\partial)/(\partial u)(sqrt(u^5+v^7)) ?
The answer to (\partial)/(\partial u)(sqrt(u^5+v^7)) is (5u^4)/(2sqrt(u^5+v^7))