A convenient expression of the time-derivative
zn(k)(t)
, of arbitrary order <i>k</i>, of the zero <i>z
<sub>n</sub>
</i>(<i>t</i>) of a time-dependent polynomial <i>p
<sub>N</sub>
</i>(<i>z</i>;<i>t</i>) of arbitrary degree <i>N</i> in <i>z</i>, and solvable dynamical systems