It is given that
\(x=\sin ^{-1} t \quad \text { and } \quad y=t \cos ^{-1} t, \quad \text { for } 0 \leqslant t\lt 1 .\)
(a) Show that \(\frac{\mathrm{d} y}{\mathrm{~d} x}=-t+\sqrt{1-t^{2}} \cos ^{-1} t\).
(b) Find \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) in terms of \(t\).