If $y = \cot^{-1} \begin{bmatrix} \tan ( \frac{\pi}{2} - x ) \end{bmatrix}$, then $\frac{dy}{dx}$ is equal to :

Question

( A ) $\frac{1}{1+x^2}$
( B ) $2$
( C ) $1$
( D ) $-\frac{1}{1+x^2}$