What is (\partial)/(\partial x)(sqrt((18)/(xy))) ?

The answer to (\partial)/(\partial x)(sqrt((18)/(xy))) is -3/(sqrt(2)x^{3/2)sqrt(y)}

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(\partial)/(\partial x)(sqrt((18)/(xy)))

\frac{\partial}{\partial x} (\frac{18}{x y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{18}{x y})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 \frac{18}{x y}} \frac{\partial}{\partial x} (\frac{18}{x y})

= \frac{1}{2 \frac{18}{x y}} \frac{\partial}{\partial x} (\frac{18}{x y})

\frac{\partial}{\partial x} (\frac{18}{x y}) = - \frac{18}{y x ^{2}}

= \frac{1}{2 \frac{18}{x y}} (- \frac{18}{y x ^{2}})

Simplify

\frac{1}{2 \frac{18}{x y}} (- \frac{18}{y x ^{2}}) : - \frac{3}{2 x ^{\frac{3}{2}} y}

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

\int_{1}^{6} k x d x

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

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

\int_{0}^{1} 6 x d x

y = e^{x}, y = x^{2} - 1, x = - 1, x = 1

What is (\partial)/(\partial x)(sqrt((18)/(xy))) ?
The answer to (\partial)/(\partial x)(sqrt((18)/(xy))) is -3/(sqrt(2)x^{3/2)sqrt(y)}