A finite-time-convergent differentiator is presented that is based on singular perturbation technique. The merits of this differentiator exist in three aspects: rapidly finite-time convergence compared with other typical differentiators; no chattering phenomenon; and besides the derivatives of the derivable signals, the generalized derivatives of some classes of signals can be obtained-for example, the generalized derivative of a triangular wave is square wave, etc. The theoretical results are confirmed by computer simulations.