# How do you find the derivative of sqrt[ x^3]?

Jun 6, 2016

Doing the derivative of the power.

#### Explanation:

$\sqrt{{x}^{3}} = {x}^{\frac{3}{2}}$.

We can use the derivative of a power that says

$\frac{d}{\mathrm{dx}} {x}^{n} = n {x}^{n - 1}$

For us $n = \frac{3}{2}$

$\frac{d}{\mathrm{dx}} {x}^{\frac{3}{2}} = \frac{3}{2} {x}^{\frac{3}{2} - 1} = \frac{3}{2} {x}^{\frac{1}{2}} = \frac{3}{2} \sqrt{x}$.