For a real number $t >0$, let $\sqrt{t}$ denote the positive square root of $t$. For a real number $x > 0$, let $F(x)= \int_{x^{2}}^{4x^{2}} \sin \sqrt{t} dt$. If $F'$ is the derivative of $F$, then
- $F'(\frac{\pi}{2}) = 0$
- $F'(\frac{\pi}{2}) = \pi$
- $F'(\frac{\pi}{2}) = - \pi$
- $F'(\frac{\pi}{2}) = 2\pi$