2 It is given that \(y = \ln ( a x + 1 )\), where \(a\) is a positive constant. Prove by mathematical induction that, for every positive integer \(n\),
$$\frac { \mathrm { d } ^ { n } y } { \mathrm {~d} x ^ { n } } = ( - 1 ) ^ { n - 1 } \frac { ( n - 1 ) ! a ^ { n } } { ( a x + 1 ) ^ { n } }$$
2 It is given that $y = \ln ( a x + 1 )$, where $a$ is a positive constant. Prove by mathematical induction that, for every positive integer $n$,
$$\frac { \mathrm { d } ^ { n } y } { \mathrm {~d} x ^ { n } } = ( - 1 ) ^ { n - 1 } \frac { ( n - 1 ) ! a ^ { n } } { ( a x + 1 ) ^ { n } }$$
\hfill \mbox{\textit{CAIE FP1 2019 Q2}}