(** Composition of functions *)
Section Comp.
Context {K : AbsRing} {V : NormedModule K}.

(* Specifications: *)
Lemma is_derive_comp :
forall (f : K -> V) (g : K -> K) (x : K) (df : V) (dg : K),
is_derive f (g x) df ->
is_derive g x dg ->
is_derive (fun x => f (g x)) x (scal dg df).
Lemma ex_derive_comp :
forall (f : K -> V) (g : K -> K) (x : K),
ex_derive f (g x) ->
ex_derive g x ->
ex_derive (fun x => f (g x)) x.