Definability of derivations in the reducts of differentially closed fields

Let $\mathcal{F}=(F;+,\cdot,0,1,D)$ be a differentially closed field. We consider the question of definability of the derivation $D$ in reducts of $\mathcal{F}$ of the form $\mathcal{F}_{R}=(F;+,\cdot,0,1,P)_{P \in R}$ where $R$ is a collection of definable sets in $\mathcal{F}$. We give examples and non-examples and establish some criteria for definability of $D$. Finally, using the tools developed in the paper we prove that under the assumption of inductiveness of $Th(\mathcal{F}_{R})$ model completeness is a necessary condition for definability of $D$. This can be seen as part of a broader project where one is interested in finding Ax-Schanuel type inequalities (or predimension inequalities) for differential equations.