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June 30th, 2016, 12:06 PM   #1
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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?
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June 30th, 2016, 12:40 PM   #2
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if $\displaystyle f(x) = \int_a^u g(t) \, dt$, where $u$ is a function of $x$ and $a$ is a constant ...

then, $f'(x) = g(u) \cdot \dfrac{du}{dx}$
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July 2nd, 2016, 04:59 PM   #3
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so I got this...

f'(x) = (14x^2-1)^12

is that right?
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July 2nd, 2016, 05:28 PM   #4
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Quote:
Originally Posted by Spectre90 View Post
so I got this...

f'(x) = (14x^2-1)^12

is that right?
No.

$f'(x) = [14(x^2)^2 - 1]^{12} \cdot 2x$
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July 2nd, 2016, 09:30 PM   #5
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You got the 2x from the derivative of x^2?
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July 3rd, 2016, 01:05 AM   #6
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Quote:
Originally Posted by Spectre90 View Post
You got the 2x from the derivative of x^2?
Have another look at post #2 ...
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