What is (\partial)/(\partial y)(sqrt(x/y)) ?

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

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(\partial)/(\partial y)(sqrt(x/y))

\frac{\partial}{\partial y} (\frac{x}{y})

- \frac{x}{2 y ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial y} (\frac{x}{y})

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 \frac{x}{y}} \frac{\partial}{\partial y} (\frac{x}{y})

= \frac{1}{2 \frac{x}{y}} \frac{\partial}{\partial y} (\frac{x}{y})

\frac{\partial}{\partial y} (\frac{x}{y}) = - \frac{x}{y ^{2}}

= \frac{1}{2 \frac{x}{y}} (- \frac{x}{y ^{2}})

Simplify

\frac{1}{2 \frac{x}{y}} (- \frac{x}{y ^{2}}) : - \frac{x}{2 y ^{\frac{3}{2}}}

= - \frac{x}{2 y ^{\frac{3}{2}}}

\frac{4083}{1 + 6.22 e ^{- 0.32 x}}

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\int 24 x^{2} (6 - 5 x^{3})^{7} d x

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