If $x= \cos^{-1} \bigg( \large\frac{1}{\sqrt {1+t^2}}\bigg) $ and $\; y= \sin ^{-1} \bigg( \large\frac{1}{\sqrt {1+t^2}}\bigg) $ then $\large\frac{dy}{dx}$

Question

$(a)\;\frac{-\sqrt {1+t^2}}{t} \\ (b)\;-1 \\ (c)\;\frac{\sqrt {1+t^2}}{t} \\ (d)\;1 $