# How do you find the derivative of sqrt(1/x^3)?

##### 2 Answers
Oct 8, 2016

i think the simplest thing is to rewrite it so that we can use the power rule.

#### Explanation:

$\sqrt{\frac{1}{x} ^ 3} = \frac{1}{\sqrt{{x}^{3}}} = \frac{1}{x} ^ \left(\frac{3}{2}\right) = {x}^{- \frac{3}{2}}$

So the derivative is

$- \frac{3}{2} {x}^{\left(- \frac{3}{2} - 1\right)} = - \frac{3}{2} {x}^{- \frac{5}{2}} = - \frac{3}{2 \sqrt{{x}^{5}}} = - \frac{3}{2 {x}^{2} \sqrt{x}}$

Oct 8, 2016

-3/(2x^(5/2)

#### Explanation:

Start by rewriting the function as.

$y = \sqrt{\frac{1}{{x}^{3}}} = {\left(\frac{1}{x} ^ 3\right)}^{\frac{1}{2}} = \frac{1}{{x}^{\frac{3}{2}}} = {x}^{- \frac{3}{2}}$

now differentiate using the $\textcolor{b l u e}{\text{power rule}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{3}{2} {x}^{- \frac{5}{2}} = - \frac{3}{2 {x}^{\frac{5}{2}}}$