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

The answer to (\partial)/(\partial u)(sqrt(u*v)) is (sqrt(v))/(2sqrt(u))

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

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

\frac{v}{2 u}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 uv} v

Simplify

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

= \frac{v}{2 u}

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What is (\partial)/(\partial u)(sqrt(u*v)) ?
The answer to (\partial)/(\partial u)(sqrt(u*v)) is (sqrt(v))/(2sqrt(u))