(** * Definitions on [R] *)

Definition Derive (f : R -> R) (x : R) := real (Lim (fun h => (f (x+h) - f x)/h) 0).

Lemma ex_derive_plus : forall (f g : K -> V) (x : K), ex_derive f x -> ex_derive g x -> ex_derive (fun x => plus (f x) (g x)) x.