(** ** Derivative of arccosine *)

(* Specifications: *)
Lemma derivable_pt_acos : forall x, -1 < x < 1 ->
derivable_pt acos x.
Lemma derive_pt_acos : forall (x : R) (Hxrange : -1 < x < 1),
derive_pt acos x (derivable_pt_acos x Hxrange) = -1 / sqrt (1 - x²).
Lemma sin_gt_x x : x < 0 -> x < sin x.