Finite differences are shown to be applicable to the on-line estimation of arbitrary-order derivatives in homogeneous discontinuous control. An output-feedback controller is produced from any finite-time-stable r-sliding homogeneous controller, capable to control the output of any smooth uncertain single-input-single-output system of a known permanent relative degree r. Variable sampling step feedback is proposed, in the absence of noises providing for the utmost r-sliding accuracy corresponding to the minimal possible sampling interval. In the presence of noises the tracking accuracy is proportional to the unknown noise magnitude. Theoretical results are confirmed by computer simulation.