5.
$$y = \mathrm { e } ^ { 3 x } \sin x$$
- Use Leibnitz's theorem to show that
$$\frac { \mathrm { d } ^ { 4 } y } { \mathrm {~d} x ^ { 4 } } = 28 \mathrm { e } ^ { 3 x } \sin x + 96 \mathrm { e } ^ { 3 x } \cos x$$
- Hence express \(\frac { \mathrm { d } ^ { 4 } y } { \mathrm {~d} x ^ { 4 } }\) in the form
$$\operatorname { Re } ^ { 3 \mathrm { x } } \sin ( \mathrm { x } + \alpha )$$
where \(R\) and \(\alpha\) are constants to be determined, \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\)