# How do you differentiate g(x) =e^x (x^3 + 4)  using the product rule?

Jan 23, 2016

$g ' \left(x\right) = {e}^{x} \left({x}^{3} + 3 {x}^{2} + 4\right)$

#### Explanation:

The product rule states that

$g ' \left(x\right) = \left({x}^{3} + 4\right) \frac{d}{\mathrm{dx}} \left[{e}^{x}\right] + {e}^{x} \frac{d}{\mathrm{dx}} \left[{x}^{3} + 4\right]$

Find each derivative.

$g ' \left(x\right) = \left({x}^{3} + 4\right) {e}^{x} + {e}^{x} \left(3 {x}^{2}\right)$

Factor a common ${e}^{x}$ term.

$g ' \left(x\right) = {e}^{x} \left({x}^{3} + 3 {x}^{2} + 4\right)$