Homework Help: Calculus AB (AP)

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.

Calculus AB (AP) - A, Tuesday, May 7, 2013 at 8:40pm
1) 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)).

Answer this Question

Related Questions

ap calculus - How is the ap calculus AB and BC test? Is there any online ...
Math (Calculus AB) - For x≠0, the slope of the tangent to y=xcosx ...
Math (Calculus AB) - For x≠0, the slope of the tangent to y=xcosx ...
AP Calculus AB - The sum of x and y is 8. What is the maximum value of xy-x^2? ...
ALL OF JISHKA STAFF - Hello I had a couple of questions and was woundering if ...
Physics - Please help!!! Physics test!? I have a physics test tomorrow on ...
AP PSYCHOLOGY - I have an AP Psychology test tomorrow and I would like practice ...
calculus please help - what is the integral of x/(1+x^2)^2 dx This is a question...
trig - hi, I have a placement test coming up tomorrow, and I'm pretty ...
physics - thanks for the help earlier just got a question I'm taking AP ...

For Further Reading

First Name:
School Subject:
Answer: