A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t {displaystyle t,} . A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t {displaystyle t,} . A variety of notations are used to denote the time derivative. In addition to the normal (Leibniz's) notation,