# How do you differentiate  f(x)= (xe^x+4)^3  using the chain rule.?

May 27, 2018

= $3 {e}^{x} \left(x + 1\right) {\left(x {e}^{x} + 4\right)}^{2}$ or some version of that

#### Explanation:

This is the chain rule.
${\left(x {e}^{x} + 4\right)}^{3}$
dy/dx = $3 {\left(x {e}^{x} + 4\right)}^{2}$ x (derivative of the inside)

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

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

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