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

The answer to (\partial)/(\partial v)(sqrt(u/v)) is -(sqrt(u))/(2v^{3/2)}

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

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

- \frac{u}{2 v ^{\frac{3}{2}}}

Solution steps

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

Treat

u

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial v} (\frac{u}{v}) = - \frac{u}{v ^{2}}

= \frac{1}{2 \frac{u}{v}} (- \frac{u}{v ^{2}})

Simplify

\frac{1}{2 \frac{u}{v}} (- \frac{u}{v ^{2}}) : - \frac{u}{2 v ^{\frac{3}{2}}}

= - \frac{u}{2 v ^{\frac{3}{2}}}

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

\frac{1}{2} (e^{x} + e^{- x})

\int sin (x + y) d x

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

f (x) = \frac{4 x + 4}{3 x ^{\frac{2}{3}}}

What is (\partial)/(\partial v)(sqrt(u/v)) ?
The answer to (\partial)/(\partial v)(sqrt(u/v)) is -(sqrt(u))/(2v^{3/2)}