How do you differentiate f(x)= (5+3x^2)*e^x  using the product rule?

Dec 4, 2015

$f ' \left(x\right) = {e}^{x} \left(3 {x}^{2} + 6 x + 5\right)$

Explanation:

According to the product rule::

$f ' \left(x\right) = {e}^{x} \frac{d}{\mathrm{dx}} \left[5 + 3 {x}^{2}\right] + \left(5 + 3 {x}^{2}\right) \frac{d}{\mathrm{dx}} \left[{e}^{x}\right]$

$f ' \left(x\right) = 6 x {e}^{x} + 5 {e}^{x} + 3 {x}^{2} {e}^{x}$

$f ' \left(x\right) = {e}^{x} \left(3 {x}^{2} + 6 x + 5\right)$