Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(y = x \mathrm { e } ^ { 2 x }\).
Find an equation of the tangent to the curve \(y = x \mathrm { e } ^ { 2 x }\) at the point \(\left( 1 , \mathrm { e } ^ { 2 } \right)\).
Given that \(y = \frac { 2 \sin 3 x } { 1 + \cos 3 x }\), use the quotient rule to show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { k } { 1 + \cos 3 x }$$
where \(k\) is an integer.