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February 1, 2015

February 1, 2015

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

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.

- Calculus AB (AP) -
**A**, Tuesday, May 7, 2013 at 8:40pm1) d/dx e^(u) is always (u')(e^(u)). In other words, take the original function and multiply it by the derivative of u (f(x)).

2) The 2nd FTC: Take the b (top number of the integral) and plug that in for t. Multiply by the derivative of b. b'(f(b)).

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