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

1 Answer
Jan 9, 2016

Answer:

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))#