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June 30th, 2016, 12:06 PM  #1 
Newbie Joined: Jun 2016 From: Somewhere Posts: 9 Thanks: 0  The Fundamental Theorem of Calculus problem.
Use the Fundamental Theorem of Calculus to find the derivative of f(x)=∫ (14t^2−1)12 dt from (4, x^2) f′(x) = ??? Do I just put x^2 over the t? then the same with 4? 
June 30th, 2016, 12:40 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 
if $\displaystyle f(x) = \int_a^u g(t) \, dt$, where $u$ is a function of $x$ and $a$ is a constant ... then, $f'(x) = g(u) \cdot \dfrac{du}{dx}$ 
July 2nd, 2016, 04:59 PM  #3 
Newbie Joined: Jun 2016 From: Somewhere Posts: 9 Thanks: 0 
so I got this... f'(x) = (14x^21)^12 is that right? 
July 2nd, 2016, 05:28 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575  
July 2nd, 2016, 09:30 PM  #5 
Newbie Joined: Jun 2016 From: Somewhere Posts: 9 Thanks: 0 
You got the 2x from the derivative of x^2?

July 3rd, 2016, 01:05 AM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575  

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