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.

Lemma derive_pt_scal :
forall f (a x:R) (pr:derivable_pt f x),
derive_pt (mult_real_fct a f) x (derivable_pt_scal _ _ _ pr) =
a * derive_pt f x pr.