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

The answer to (\partial)/(\partial x)(sqrt(x/y)) is 1/(2sqrt(x)\sqrt{y)}

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

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

\frac{1}{2 x y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{x}{y}} \cdot \frac{1}{y}

Simplify

\frac{1}{2 \frac{x}{y}} \cdot \frac{1}{y} : \frac{1}{2 x y}

= \frac{1}{2 x y}

\int_{- 1}^{1} e^{x^{2}} d x

\int x^{4} - 2 x^{2} - 4 x d x

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

\frac{d}{d x} ((x^{2} - 2)^{- 3})

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

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