4 The equation of a curve is given by \(\mathrm { e } ^ { 2 y } = 1 + \sin x\).
- By differentiating implicitly, find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
- Find an expression for \(y\) in terms of \(x\), and differentiate it to verify the result in part (i).