  We establish a correspondence between automorphisms and derivations on
certain algebras of generalised power series. In particular, we describe a Lie
algebra of derivations on a field $k(\!(G)\!)$ of generalised power series,
exploiting our knowledge of its group of valuation preserving automorphisms.
The correspondence is given by the formal Taylor expansion of the exponential.
In order to define the exponential map, we develop an appropriate notion of
summability of infinite families in algebras. We show that there is a large
class of algebras in which the exponential induces the above correspondence.
