(** * Definitions on [R] *)

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

Lemma Derive_inv (f : R -> R) (x : R) : ex_derive f x -> f x <> 0 -> Derive (fun y => / f y) x = - Derive f x / (f x) ^ 2.