  We study the class of differentially henselian fields, which are henselian
valued fields equipped with generic derivations in the sense of Cubides
Kovacics and Point, and are special cases of differentially large fields in the
sense of Le\'on S\'anchez and Tressl. We prove that many results from henselian
valued fields as well as differentially large fields can be lifted to the
differentially henselian setting, for instance Ax-Kochen/Ershov principles,
characterisations in terms of differential algebras, etc. We also give methods
to concretely construct such fields in terms of iterated power series
expansions and inductive constructions on transcendence bases.
