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

Apr 1, 2016

$2 {e}^{x} + x + \left(x - 2\right) \left(2 {e}^{x} + 1\right)$

#### Explanation:

Differentiate using the $\textcolor{b l u e}{\text{ product rule }}$

If f(x) = g(x).h(x) then f'(x) = g(x).h'(x) + h(x).g'(x)

the standard derivative : $\frac{d}{\mathrm{dx}} \left({e}^{x}\right) = {e}^{x}$
$\text{ ----------------------------------------------------}$

g(x) = $2 {e}^{x} + x \Rightarrow g ' \left(x\right) = 2 {e}^{x} + 1$

and h(x) = x - 2 $\Rightarrow h ' \left(x\right) = 1$
$\text{ -------------------------------------------------}$

Substituting these values into f'(x)

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