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_mult :
forall f1 f2 (x:R) (pr1:derivable_pt f1 x) (pr2:derivable_pt f2 x),
derive_pt (f1 * f2) x (derivable_pt_mult _ _ _ pr1 pr2) =
derive_pt f1 x pr1 * f2 x + f1 x * derive_pt f2 x pr2.