$f(x)=\sin \frac{x}{2}$ হলে $f^{\prime}\left(\frac{\pi}{2}\right)=$ কত?

$\frac{-1}{2 \sqrt{2}}$

$\frac{-1}{4 \sqrt{2}}$

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{2}}$