# How do you differentiate g(x) = (2 + 4e^x) ( 2x + 2x^2) using the product rule?

$g ' \left(x\right) = 4 {e}^{x} \left(2 x + 2 {x}^{2}\right) + \left(4 x + 2\right) \left(2 + 4 {e}^{x}\right)$
$g$ is the product of two functions $u \left(x\right) = 2 + 4 {e}^{x}$ and $v \left(x\right) = 2 x + 2 {x}^{2}$
By the product rule, $g ' = u ' v + u v '$. Here, $u ' \left(x\right) = 4 {e}^{x}$ and $v ' \left(x\right) = 4 x + 2$.