derivative

derivative Rate of change of the value of a mathematical function with respect to a change in the independent variable. The derivative is an expression of the instantaneous rate of change of the function's value: in general it is itself a function of the variable. An example is obtaining the velocity and acceleration of an object that moves distance x in time t according to the equation x = atⁿ. In such motion, the velocity increases with time. The expression dx/dt, called the first derivative of distance with respect to time, is equal to the velocity of the object; in this example it equals nat⁽ⁿ⁻¹⁾. The result is obtained by differential calculus. In this example, the second derivative, written d²x/dt², is equal to the acceleration.