The rapid growth of information technology is closely linked to our ability to modulate and demodulate a signal, whether in the frequency or in the time domain. Recent demonstrations of terahertz (THz) modulation involve active semiconductor metamaterial surfaces or use of a grating-based micromirror for frequency offset tuning. However, a wideband and active differentiator in the THz frequency band is yet to be demonstrated. Here, we propose a simple method to differentiate a THz pulse by inducing tiny phase changes on the THz beam path using a piezoelectric micromachined ultrasonic transducer array. We precisely demonstrate that the modulated THz signal detected after the piezoelectric device is proportional to the first-order derivative of the THz pulse. The proposed technique will be able to support a wide range of THz applications, such as peak detection schemes for telecommunication systems.