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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, $f'(x) = g(u) \cdot \dfrac{du}{dx}$ Thanks from Country Boy
 July 2nd, 2016, 04:59 PM #3 Newbie   Joined: Jun 2016 From: Somewhere Posts: 9 Thanks: 0 so I got this... f'(x) = (14x^2-1)^12 is that right?
July 2nd, 2016, 05:28 PM   #4
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Quote:
 Originally Posted by Spectre90 so I got this... f'(x) = (14x^2-1)^12 is that right?
No.

$f'(x) = [14(x^2)^2 - 1]^{12} \cdot 2x$

 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
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Quote:
 Originally Posted by Spectre90 You got the 2x from the derivative of x^2?
Have another look at post #2 ...

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