It is given that
\(x=1+\frac{1}{t} \quad \text { and } \quad y=\cos ^{-1} t \quad \text { for } 0\lt t\lt 1 .\)
(a) Show that \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{t^{2}}{\sqrt{1-t^{2}}}\).
(b) Show that \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=-t^{a}\left(1-t^{2}\right)^{b}\left(2-t^{2}\right)\), where \(a\) and \(b\) are constants to be determined.