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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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 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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 Originally Posted by Spectre90 You got the 2x from the derivative of x^2?
Have another look at post #2 ... Tags calculus, fundamental, problem, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Mr Davis 97 Calculus 1 April 16th, 2015 04:06 PM bonildo Calculus 2 September 11th, 2014 10:00 AM Mr Davis 97 Calculus 6 June 5th, 2014 02:29 PM MadSoulz Real Analysis 2 April 15th, 2014 03:19 PM riotsandravess Calculus 3 November 25th, 2010 12:44 PM

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