If $y= \sec (\tan ^{-1}x)$, then $\large\frac{dy}{dx}$ at $x=1$ is equal to :

Question

$\begin{array}{1 1} (1) \large\frac{1}{\sqrt 2} \\ (2) \frac{1}{2} \\ (3) 1 \\ (4) \sqrt 2 \end {array}$