  Firstly we establish a sharp pointwise estimate for the arbitrary derivative
of the function $f\in F_{\alpha}^{p},$ where $F_{\alpha}^{p}$ denotes the Fock
space for $1\leq p<\infty.$ Then, in a particular Hilbert case when $p=2$ we
establish another specific pointwise sharp estimate. We also consider the
differential operator between $F_{\alpha}^{p}$ and $F_{\beta}^{p}$ for
$\beta>\alpha$ and its adjoint.
