# How do you differentiate  f(x)= (6e^(-x)+2)^3  using the chain rule?

Dec 22, 2015

$f ' \left(x\right) = - 18 {e}^{-} x \left(6 {e}^{-} x + 2\right)$

#### Explanation:

According to the chain rule:

$f ' \left(x\right) = 3 {\left(6 {e}^{-} x + 2\right)}^{2} \frac{d}{\mathrm{dx}} \left[6 {e}^{-} x + 2\right]$

Once again applying the chain rule:

$\frac{d}{\mathrm{dx}} \left[6 {e}^{-} x + 2\right] = 6 {e}^{-} x \frac{d}{\mathrm{dx}} \left[- x\right]$

$\implies - 6 {e}^{-} x$

Thus,

$f ' \left(x\right) = - 18 {e}^{-} x \left(6 {e}^{-} x + 2\right)$