# How do you differentiate f(x) = ( 4x - 3) ( xe^x) using the product rule?

$f ' \left(x\right) = {e}^{x} \cdot \left(4 {x}^{2} + 5 x - 3\right)$

#### Explanation:

from the given

f(x)=(4x-3)(x*e^x)#

$f ' \left(x\right) = \left(4 x - 3\right) \left(1 \cdot {e}^{x} + x \cdot {e}^{x}\right) + x \cdot {e}^{x} \cdot 4$

$f ' \left(x\right) = {e}^{x} \cdot \left(1 + x\right) \left(4 x - 3\right) + 4 x \cdot {e}^{x}$

$f ' \left(x\right) = {e}^{x} \left(\left(x + 1\right) \left(4 x - 3\right) + 4 x\right)$

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

$f ' \left(x\right) = {e}^{x} \left(4 {x}^{2} + 5 x - 3\right)$