6 A curve has parametric equations
$$x = \frac { \mathrm { e } ^ { 2 t } - 2 } { \mathrm { e } ^ { 2 t } + 1 } , \quad y = \mathrm { e } ^ { 3 t } + 1$$
- Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
\includegraphics[max width=\textwidth, alt={}, center]{dcc483e9-630e-4f02-ad8c-4a27c0720fc6-10_2718_42_107_2007}
\includegraphics[max width=\textwidth, alt={}, center]{dcc483e9-630e-4f02-ad8c-4a27c0720fc6-11_2725_35_99_20} - Find the exact gradient of the curve at the point where the curve crosses the \(y\)-axis.