Abstract: Let T be a model complete o-minimal theory which extends the theory of real closed ordered fields (RCF). We introduce T-derivations: derivations on models of T which cooperate with T-definable functions. The theory of models of T expanded by a T-derivation has a model completion, in which the derivation acts “generically.” If T = RCF, then this model completion is the theory of closed ordered differential fields (CODF) as introduced by Singer. We can recover many of the known facts about CODF (open core, distality) in our setting. We can also describe thorn-rank for models of T with a generic T-derivation. This is joint work with Antongiulio Fornasiero.