2 A curve has parametric equations \(x = \mathrm { e } ^ { 3 t } , y = t \mathrm { e } ^ { 2 t }\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\). Hence find the exact gradient of the curve at the point with parameter \(t = 1\).
- Find the cartesian equation of the curve in the form \(y = a x ^ { b } \ln x\), where \(a\) and \(b\) are constants to be determined.