Find the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at the point on \(C\) where \(t = \frac { 2 } { 3 }\).
Show that \(x = \frac { 4 - \mathrm { e } ^ { 2 - 6 t } } { 4 }\) can be rearranged into the form \(\mathrm { e } ^ { 3 t } = \frac { \mathrm { e } } { 2 \sqrt { ( 1 - x ) } }\).
Hence find the Cartesian equation of \(C\), giving your answer in the form
$$y = \frac { \mathrm { e } } { \mathrm { f } ( x ) [ 1 - \ln ( \mathrm { f } ( x ) ) ] }$$