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 derivable_scal :
forall f (a:R), derivable f -> derivable (mult_real_fct a f).