The derivative is a measure of change of one quantity in response to change in another quantity. The process of finding a derivative is called differentiation. The differentiation is used to find the rate of change of one quantity with respect to another quantity. For example, velocity is change of position with respect to time. The slope of a line is the rate of change of y with respect to x.
The derivative of a function f with respect to variable x is written as df/dx or f’(x). The differentiation of y with respect to x can also be shown as Δy/Δx. The greek symbol Δ (delta) is an abbreviation for ‘change in’.
The derivative of a function f(x) with respect to variable x is
Below are derivatives of some simple functions:
