If $f(x)=\sqrt{\operatorname{Cos}^{-1} \sqrt{1-x^2}}$, then $f^{\prime}\left(\frac{1}{2}\right)=$

• Correct answer
  A

  $\sqrt{\frac{2}{\pi}}$
• B

  $\sqrt{\frac{\pi}{2}}$
• C

  $-\sqrt{\frac{2}{\pi}}$
• D

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

Hence, the correct answer is option: 'A'.