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_pt_mult :
forall f1 f2 (x:R),
derivable_pt f1 x -> derivable_pt f2 x -> derivable_pt (f1 * f2) x.