If $f(x) = \begin{vmatrix} 2 \cos x & 1 & 0 \\ x - \frac{\pi}{2} & 2 \cos x & 1 \\ 0 & 1 & 2 \cos x \end{vmatrix}$, then $\frac{df}{dx}$ at $x = \frac{\pi}{2}$ is:

Question

( A ) 1
( B ) 2
( C ) $\frac{\pi}{2}$
( D ) 8