It is given that
\(x=1+\frac{1}{t} \quad \text { and } \quad y=t \mathrm{e}^{t} .\)
(a) Show that \(\frac{\mathrm{d} y}{\mathrm{~d} x}=-\mathrm{e}^{t}\left(t^{3}+t^{2}\right)\).
(b) Find \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) in terms of \(t\).