(** Addition of functions *)
Section Plus.
Context {K : AbsRing} {V : NormedModule K}.

Lemma ex_derive_sum_n :
forall (f : nat -> K -> V) (n : nat) (x : K),
(forall k, (k <= n)%nat -> ex_derive (f k) x) ->
ex_derive (fun y => sum_n (fun k => f k y) n) x.