What is (\partial)/(\partial v)(sqrt(v/u)) ?

The answer to (\partial)/(\partial v)(sqrt(v/u)) is 1/(2sqrt(v)\sqrt{u)}

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(\partial)/(\partial v)(sqrt(v/u))

\frac{\partial}{\partial v} (\frac{v}{u})

\frac{1}{2 v u}

Solution steps

\frac{\partial}{\partial v} (\frac{v}{u})

Treat

u

as a constant

Apply the chain rule:

\frac{1}{2 \frac{v}{u}} \frac{\partial}{\partial v} (\frac{v}{u})

= \frac{1}{2 \frac{v}{u}} \frac{\partial}{\partial v} (\frac{v}{u})

\frac{\partial}{\partial v} (\frac{v}{u}) = \frac{1}{u}

= \frac{1}{2 \frac{v}{u}} \cdot \frac{1}{u}

Simplify

\frac{1}{2 \frac{v}{u}} \cdot \frac{1}{u} : \frac{1}{2 v u}

= \frac{1}{2 v u}

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What is (\partial)/(\partial v)(sqrt(v/u)) ?
The answer to (\partial)/(\partial v)(sqrt(v/u)) is 1/(2sqrt(v)\sqrt{u)}