What is (\partial)/(\partial x)(sqrt((16)/(xy))) ?

The answer to (\partial)/(\partial x)(sqrt((16)/(xy))) is -2/(x^{3/2)sqrt(y)}

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(\partial)/(\partial x)(sqrt((16)/(xy)))

\frac{\partial}{\partial x} (\frac{16}{x y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{16}{x y})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{16}{x y}} \frac{\partial}{\partial x} (\frac{16}{x y})

= \frac{1}{2 \frac{16}{x y}} \frac{\partial}{\partial x} (\frac{16}{x y})

\frac{\partial}{\partial x} (\frac{16}{x y}) = - \frac{16}{y x ^{2}}

= \frac{1}{2 \frac{16}{x y}} (- \frac{16}{y x ^{2}})

Simplify

\frac{1}{2 \frac{16}{x y}} (- \frac{16}{y x ^{2}}) : - \frac{2}{x ^{\frac{3}{2}} y}

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

\int_{0}^{2} \frac{5}{( x - 1 ) ^{\frac{1}{3}}} d x

x \to 2 lim (\frac{x ^{2} + 5}{x - 2})

\frac{\partial}{\partial y} (8 x y + 8 y^{2} - 2 x + 2 y - 1)

\frac{d}{d x} ((1 + \frac{5}{x})^{x})

\frac{\partial}{\partial z} (x e^{2 y + 3 z})

What is (\partial)/(\partial x)(sqrt((16)/(xy))) ?
The answer to (\partial)/(\partial x)(sqrt((16)/(xy))) is -2/(x^{3/2)sqrt(y)}