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

Dec 9, 2015

$f ' \left(x\right) = 2 {x}^{2} {e}^{x}$

#### Explanation:

The product rule states that
$\frac{d}{\mathrm{dx}} \left[f \left(x\right) \cdot g \left(x\right)\right] = f \left(x\right) \cdot g ' \left(x\right) + g \left(x\right) \cdot f ' \left(x\right)$.

Using this rule, together with other standard rules of differentiation yields

$\frac{d}{\mathrm{dx}} \left(2 {x}^{2} - 4 x + 4\right) {e}^{x} = \left(2 {x}^{2} - 4 x + 4\right) {e}^{x} + \left(4 x - 4\right) {e}^{x}$

$= {e}^{x} \left(2 {x}^{2}\right)$