How do you use the Product Rule to find the derivative of ?

Sep 26, 2015

See the explanation.

Explanation:

$h \left(x\right) = f \left(x\right) \cdot g \left(x\right)$

$h ' \left(x\right) = f ' \left(x\right) \cdot g \left(x\right) + f \left(x\right) \cdot g ' \left(x\right)$

Example:

$h = \left({x}^{4} - 5 {x}^{2} + 1\right) {e}^{x}$

$f = {x}^{4} - 5 {x}^{2} + 1 \implies f ' = 4 {x}^{3} - 10 x$
$g = {e}^{x} \implies g ' = {e}^{x}$

$h ' = \left(4 {x}^{3} - 10 x\right) {e}^{x} + \left({x}^{4} - 5 {x}^{2} + 1\right) {e}^{x}$

$h ' = \left({x}^{4} + 4 {x}^{3} - 5 {x}^{2} - 10 x + 1\right) {e}^{x}$