- (a) Write down the Maclaurin series of \(\mathrm { e } ^ { x }\), in ascending power of \(x\), up to and including the term in \(x ^ { 3 }\)
(b) Hence, without differentiating, determine the Maclaurin series of
$$\mathrm { e } ^ { \left( \mathrm { e } ^ { x } - 1 \right) }$$
in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\), giving each coefficient in simplest form.