In calculus, differentiation is the process of finding the derivative of a function. The derivative of a function of a single variable at a chosen input value is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable.

Differentiation is finding the slope of a function, which represents how fast something is changing at an instant. For example, the derivative of position of a moving object with respect to time is the objects velocity, and the derivative of velocity with respect to time is acceleration.

To differentiate a function means to find its rate of change function. For instance, if you have a function that describes the position of a car at any time, then the derivative of this function tells you the rate of change, i.e., speed, of the car at any time.

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 basic rules for differentiating the sum, product, or quotient of any two functions.