How do you differentiate f(x)=(4e^x+1)(x^2-3) using the product rule?

Jun 5, 2018

$f ' \left(x\right) = 4 {e}^{x} \left({x}^{2} + 2 x - 13\right) + 2 x$

Explanation:

$f \left(x\right) = \left(4 {e}^{x} + 1\right) \left({x}^{2} - 3\right)$

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left(4 {e}^{x} + 1\right) \left({x}^{2} - 3\right) + \left(4 {e}^{x} + 1\right) \frac{d}{\mathrm{dx}} \left({x}^{2} - 3\right)$
$f ' \left(x\right) = \left(4 {e}^{x}\right) \left({x}^{2} - 3\right) + \left(4 {e}^{x} + 1\right) \left(2 x\right)$
$f ' \left(x\right) = 4 {e}^{x} {x}^{2} - 12 {e}^{x} + 8 x {e}^{x} + 2 x$
$f ' \left(x\right) = 4 {e}^{x} \left({x}^{2} + 2 x - 13\right) + 2 x$