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

1 Answer
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 ( )^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))