Integral or differential

Calculus Level 3

For a real number $x > 0$, let $\large F(x) = \int_{x^2}^{4x^2} \sin\sqrt t\, dt$

For a real number $t > 0$, let $\sqrt t$ denote the positive square root of $t$. If $F'$ is the first derivative of $F$, find the value of $F'\left(\dfrac{\pi}{2}\right)$?

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