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

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

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

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

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

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (ln (\frac{9 - x}{5 + x}))

- 9 x^{2}

\frac{d}{d x} (arccos (cos (x)))

\frac{d y}{d x}, x y = x - 2 y

\frac{d y}{d x} = \frac{( x - 3 )}{y - 4}

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