Let $f : \mathbb C \to \mathbb C$ be an entire function belonging to the Fock space $F_\alpha^2$, that is, $$ \int_\mathbb{C} |f(z)|^2 e^{-\alpha|z|^2} \, dA(z) $$ with $A$ the Euclidean are measure. To which space does the complex derivative of $f$ belong, $$ f' \in F_\beta^2 $$ $\beta > 0$. Can we choose $\beta = \alpha$?