Normalized derivative of a polynomial
= Normalized derivative of a polynomial
{title2=$D_jP$}
The $j$th normalized derivative is
$$
D_jP(X)=\frac1{j!}\frac{d^jP}{dX^j}(X).
$$
If $P(X)=\sum_ra_rX^r$ has integer coefficients, then $D_jP(X)=\sum_{r\geq j}\binom rj a_rX^{r-j}$ also has integer coefficients. For $\deg P\leq n$, its <naive polynomial height> is at most $2^nH(P)$.