5.
$$y = \mathrm { e } ^ { \cos ^ { 2 } x }$$
- Show that
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = \mathrm { e } ^ { \cos ^ { 2 } x } \left( \sin ^ { 2 } 2 x - 2 \cos 2 x \right)$$
- Hence find the Maclaurin series expansion of \(\mathrm { e } ^ { \cos ^ { 2 } x }\) up to and including the term in \(x ^ { 2 }\)