Suppose that http://webwork.asu.edu/webwork2_file...8892547241.png, where Find http://webwork.asu.edu/webwork2_file...4e90f0b0a1.png.

Does anyone know who to go about getting the second derivative from those two functions?

Thank you

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- Dec 8th 2009, 09:12 AMmybrohshi5Second derivative
Suppose that http://webwork.asu.edu/webwork2_file...8892547241.png, where Find http://webwork.asu.edu/webwork2_file...4e90f0b0a1.png.

Does anyone know who to go about getting the second derivative from those two functions?

Thank you - Dec 8th 2009, 09:39 AMnehme007
$\displaystyle F'(x) = \frac{d}{dx} \int_1^x f(t) dt = f(x) $ by the fundamental theorem of calculus. So $\displaystyle F''(2) = f'(2)$.

You can find $\displaystyle f'(t) $ using the fundamental theorem of calculus as well. You should get $\displaystyle f'(t) = 4t^3 \frac{\sqrt{5+t^{16}}}{t^4} $ (there's a chain rule application in there as well).