# Second derivative

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• December 8th 2009, 09:12 AM
mybrohshi5
Second 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
• December 8th 2009, 09:39 AM
nehme007
$F'(x) = \frac{d}{dx} \int_1^x f(t) dt = f(x)$ by the fundamental theorem of calculus. So $F''(2) = f'(2)$.
You can find $f'(t)$ using the fundamental theorem of calculus as well. You should get $f'(t) = 4t^3 \frac{\sqrt{5+t^{16}}}{t^4}$ (there's a chain rule application in there as well).