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

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

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

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

\frac{1}{2 u v}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 u v}

\frac{d}{d x} ((x^{2} - 1) (- x^{2} - 4 x - 2))

\frac{\partial}{\partial x} (5 x^{2} y^{5})

\frac{\partial}{\partial y} (x y^{6} + x^{2} + y^{4})

\frac{\partial}{\partial z} (arctan (\frac{x}{z}))

- 2 x^{2} + 50 x + 25.247

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