With derivative action, the controller output is proportional to the rate of change of the measurement or error. The controller output is calculated by the rate of change of the measurement with time.
CONTROLLER OUTPUT = DERIVATIVE (dm)/(dt)
Where m is the measurement at time t.
Some manufacturers use the term rate or pre-act instead of derivative. Derivative, rate, and pre-act are the same thing.
DERIVATIVE = RATE = PRE ACT
Derivative action can compensate for a changing measurement. Thus derivative takes action to inhibit more rapid changes of the measurement than proportional action. When a load or set-point change occurs, the derivative action causes the controller gain to move the "wrong" way when the measurement gets near the set-point. Derivative is often used to avoid overshoot.
Derivative action can stabilize loops since it adds phase lead. Generally, if you use derivative action, more controller gain and reset can be used.
With a PID controller the amplitude ratio now has a dip near the center of the frequency response. Integral action gives the controller high gain at low frequencies, and derivative action causes the gain to start rising after the "dip". At higher frequencies the filter on derivative action limits the derivative action. At very high frequencies (above 314 radians/time; the Nyquist frequency) the controller phase and amplitude ratio increase and decrease quite a bit because of discrete sampling. If the controller had no filter the controller amplitude ratio would steadily increase at high frequencies up to the Nyquist frequency (1/2 the sampling frequency). The controller phase now has a hump due to the derivative lead action and filtering. (Graphic courtesy of ExperTune Loop Simulator.)
The time response is less oscillatory than with the PI controller. Derivative action has helped stabilize the loop.