$y= \sin ^{-1} \bigg[\large\frac{1-x^2}{1+x^2}\bigg],$ find $\large\frac{dy}{dx}$:

Question

\[(a)\;\frac{2}{1+x^2} \quad (b)\;\frac{-2}{1+x^2} \quad (c)\;\frac{2}{2-x^2} \quad (d)\;\frac{1}{2+x^2}\]