(** *** Composition *)
(** Composition with linear functions *)

Lemma Derive_n_comp_scal (f : R -> R) (a : R) (n : nat) (x : R) :
locally (a * x) (fun x => forall k, (k <= n)%nat -> ex_derive_n f k x) ->
Derive_n (fun y => f (a * y)) n x  = (a ^ n * Derive_n f n (a * x)).