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Posted by on Tuesday, February 9, 2010 at 9:12pm.

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!!

  • Calculus - , Tuesday, February 9, 2010 at 9:18pm

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

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

    now take the ln of both sides.

  • Calculus - , Tuesday, February 9, 2010 at 10:40pm

    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! :)

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