End Plus.

(* Specifications: *)
Lemma Derive_plus :
forall f g x, ex_derive f x -> ex_derive g x ->
Derive (fun x => f x + g x) x = Derive f x + Derive g x.
Lemma Derive_sum_n (f : nat -> R -> R) (n : nat) (x : R) :
(forall k, (k <= n)%nat -> ex_derive (f k) x) ->
Derive (fun y => sum_n (fun k => f k y) n) x = sum_n (fun k => Derive (f k) x) n.