(** * Definitions on [R] *)

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

Lemma Derive_mult (f g : R -> R) (x : R) : ex_derive f x -> ex_derive g x -> Derive (fun x => f x * g x) x = Derive f x * g x + f x * Derive g x.