(** * Definitions on [R] *)

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

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