Question

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

Answer 1

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 `( )^3`

So...

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