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We study an Unruh-DeWitt particle detector that is coupled to the proper timederivative of a real scalar field in 1+1 spacetime dimensions. Working withinfirst-order perturbation theory, we cast the transition probability into aregulator-free form, and we show that the transition rate remains well definedin the limit of sharp switching. The detector is insensitive to the infraredambiguity when the field becomes massless, and we verify explicitly theregularity of the massless limit for a static detector in Minkowski half-space.We then consider a massless field for two scenarios of interest for theHawking-Unruh effect: an inertial detector in Minkowski spacetime with anexponentially receding mirror, and an inertial detector in $(1+1)$-dimensionalSchwarzschild spacetime, in the Hartle-Hawking-Israel and Unruh vacua. In themirror spacetime the transition rate traces the onset of an energy flux fromthe mirror, with the expected Planckian late time asymptotics. In theSchwarzschild spacetime the transition rate of a detector that falls in frominfinity gradually loses thermality, diverging near the singularityproportionally to $r^{-3/2}$.

Onset and decay of the 1+1 Hawking-Unruh effect: what the derivative-coupling detector saw