Posted by **Jake** on Wednesday, April 13, 2011 at 2:47am.

Hi, I have a calculus test tomorrow and I understand how to complete all of the problems, but I am unsure behind the reasoning of taking two derivatives. Can someone please explain the following:

1. g(x)=e^(f(x))

g'(x)=e^(f(x))f'(x)

2. f(x)=Integral from 0 to 3x of the square root of (4+t^2)dt

f'(x) = 3 times the square root of (4+9x^2).

For the second derivative, I know it has something to do with the 2nd fundamental theorem of calculus, but if you could elaborate I would appreciate it greatly.

Thank you very much.

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