The rate at which velocity is changing at a given instant is described by

The rate of change of velocity with respect to time is acceleration. When we have some period of time, mathematically we write it: a=Δv/Δt, where Δv is a change in velocity and Δt is a time interval. When we talk about an instant of time, we have a limit: a=lim Δv/Δt, where Δt→0 and we write that as a=dv/dt where dv is an infinitesimal or infinitely small change in velocity and dt is an infinitesimally or infinitely small change in the time interval. So the correct answer is: the rate the velocity is changing at a given instant is acceleration.