# How do you differentiate f(x)=((65e^-7x)+2)^3  using the chain rule?

Jan 9, 2016

Take the derivative of the outside, and leave the inside alone, then multiply it by the derivative of the inside.

#### Explanation:

f(x)=((65e^(-7)x+2)^3

Outermost layer is the ${\left(\right)}^{3}$

So...

$f ' \left(x\right) = 3 {\left(65 {e}^{- 7} x + 2\right)}^{2}$ is the first piece. Then multiply that times the derivative of the inside, which, despite the confusing look of the first term, is a simple linear equation...

so...

$f ' \left(x\right) = 3 {\left(65 {e}^{- 7} x + 2\right)}^{2} \cdot \left(65 {e}^{- 7}\right)$