Suppose that , where Find .
Does anyone know who to go about getting the second derivative from those two functions?
Thank you
$\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).