# How do you differentiate f(x)= e^x(x^3-1) using the product rule?

Nov 24, 2015

$f ' \left(x\right) = {e}^{x} \left({x}^{3} + 3 {x}^{2} - 1\right)$

#### Explanation:

According to the Product Rule:

$f ' \left(x\right) = \left({x}^{3} - 1\right) \frac{d}{\mathrm{dx}} \left[{e}^{x}\right] + {e}^{x} \frac{d}{\mathrm{dx}} \left[{x}^{3} - 1\right]$

$f ' \left(x\right) = {e}^{x} \left({x}^{3} - 1\right) + 3 {x}^{2} {e}^{x}$

$f ' \left(x\right) = {e}^{x} \left({x}^{3} + 3 {x}^{2} - 1\right)$