Let $n$ in $\mathbb { N } ^ { * }$, verify that for real $x$ $$\frac { \mathrm { d } } { \mathrm {~d} x } \left( x ^ { n } \varphi _ { n } ( x ) \right) = x ^ { n } \varphi _ { n - 1 } ( x )$$
Let $n$ in $\mathbb { N } ^ { * }$, verify that for real $x$
$$\frac { \mathrm { d } } { \mathrm {~d} x } \left( x ^ { n } \varphi _ { n } ( x ) \right) = x ^ { n } \varphi _ { n - 1 } ( x )$$