3 Given that \(a\) is a constant, prove by mathematical induction that, for every positive integer \(n\),
$$\frac { \mathrm { d } ^ { n } } { \mathrm {~d} x ^ { n } } \left( x \mathrm { e } ^ { a x } \right) = n a ^ { n - 1 } \mathrm { e } ^ { a x } + a ^ { n } x \mathrm { e } ^ { a x }$$
3 Given that $a$ is a constant, prove by mathematical induction that, for every positive integer $n$,
$$\frac { \mathrm { d } ^ { n } } { \mathrm {~d} x ^ { n } } \left( x \mathrm { e } ^ { a x } \right) = n a ^ { n - 1 } \mathrm { e } ^ { a x } + a ^ { n } x \mathrm { e } ^ { a x }$$
\hfill \mbox{\textit{CAIE FP1 2015 Q3}}