How do you differentiate g(y) =(2+x )e^x  using the product rule?

May 10, 2017

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

Explanation:

Let's assume that you meant to ask how differentiate
$f \left(x\right) = \left(2 + x\right) {e}^{x}$

The product rule states

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

In the given equation, let $g \left(x\right) = 2 + x$ and $h \left(x\right) = {e}^{x}$

The derivatives are $g ' \left(x\right) = 1$ and $h ' \left(x\right) = {e}^{x}$

Plugging all four into the product rule gives

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