(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Local Open Scope R_scope.

Lemma derive_pt_div :
forall (f1 f2:R -> R) (x:R) (pr1:derivable_pt f1 x)
(pr2:derivable_pt f2 x) (na:f2 x <> 0),
derive_pt (f1 / f2) x (derivable_pt_div _ _ _ pr1 pr2 na) =
(derive_pt f1 x pr1 * f2 x - derive_pt f2 x pr2 * f1 x) / Rsqr (f2 x).