Question

Find f'(c) if f(x)=-3e^(x+2)+ e^(-5)
[NOTE:A small algebraic manipulation is needed first to get f(x) into a form so that the derivative can be taken and your answer isn't a # but rather a formula that returns and answer.]

attempt at the problem:
3e^(x+2)=e^(-5)---->ln both sides
3^(x+2)=-5
f(x)=3^(x+2)+5
so then: f'(x)=3^(x+2)*ln(3)
This answer is incorrect and I don't know what else to do. I also tried to just take the derivative without manipulating the problem and my answer was still incorrect. Please help. Thank you!!

Answer 1

-3e^(x+2)=e^(-5)

e^-3(x+2)=e^-5

now take the ln of both sides.

Answer 2

after you ln both sides you end up with
-3(x+2)=-5
-3x-6=-5
f(x)= -3x-1
f'(x)= -3
unfortunately that was not correct either, but I appreciate your help! :)