5 It is given that \(y = ( 1 + x ) ^ { 2 } \ln ( 1 + x )\). Find \(\frac { \mathrm { d } ^ { 3 } y } { \mathrm {~d} x ^ { 3 } }\). Prove by mathematical induction that, for every integer \(n \geqslant 3\), $$\frac { \mathrm { d } ^ { n } y } { \mathrm {~d} x ^ { n } } = ( - 1 ) ^ { n - 1 } \frac { 2 ( n - 3 ) ! } { ( 1 + x ) ^ { n - 2 } }$$