intros f x l a df;
apply (derivable_pt_lim_ext (fun y => a * f y)).
- intros z; rewrite Rmult_comm; reflexivity.
- unfold Rdiv; rewrite Rmult_comm; apply derivable_pt_lim_scal; assumption.
Qed.

(** ** Rules for derive_pt (derivative function on whole domain) *)
Lemma derive_pt_id : forall x:R, derive_pt id x (derivable_pt_id _) = 1.