Neostability transfers in derivation-like theories

Motivated by structural properties of differential field extensions, we introduce the notion of a theory T being derivation-like with respect to another model complete theory T₀. We prove that when T admits a model companion T₊, several model-theoretic properties transfer from T₀ to T₊. These properties include completeness, quantifier elimination, stability, simplicity, and NSOP₁. We also observe that, aside from the theory of differential fields, examples of derivation-like theories are plentiful.