  For arbitrary radial weights $w$ and $u$, we study the integration operator
between the growth spaces $H_w^\infty$ and $H_u^\infty$ on the complex plane.
Also, we investigate the differentiation operator on the Hardy growth spaces
$H_w^p$, $0<p<\infty$, defined on the unit disk or on the complex plane. As in
the case $p=\infty$, the log-convex weights $w$ play a special role in the
problems under consideration.
