Differentiation is a mathematical process of finding the derivative, or rate of change, of a function. It is a fundamental tool of calculus and is one of the two important concepts in calculus, the other being integration. The derivative shows the sensitivity of change of a functions output with respect to the input. In other words, it measures how quickly the output of a function changes when the input changes. The derivative of the position of a moving object with respect to time is the objects velocity.
Differentiation can be defined as a derivative of a function with respect to an independent variable. The rate of change of a function per unit change in the independent variable is given by the derivative. Linear functions and non-linear functions are the two categories of functions under calculus. Differentiation can be applied to measure the function per unit change in the independent variable.
The practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions. The three basic derivatives are for algebraic functions, trigonometric functions, and exponential functions. For functions built up of combinations of these classes of functions, the theory provides the following basic rules for differentiating the sum, product, or quotient of any two functions.
Differentiation is done by applying the techniques of known differentiation formulas and differentiation rules in finding the derivative of a given function. The process of finding derivatives of a function is called differentiation in calculus. The maximum or minimum value of a function, the velocity and acceleration of moving objects, and the tangent of a curve are determined by differentiation.
