A derivative of a function is a second function showing the rate of change of the dependent variable compared to the independent variable. It can be thought of as a graph of the slope of the function from which it is derived. The process of finding a derivative is called differentiation.

Let D\subseteq\R and f:D\to\R be a function. Then the derivative of f is a function f':D'\to\R defined by:

The derivative is undefined when this limit does not exist, that is, f is not differentiable.


A simpler way of finding the derivative is to multiply the coefficient by the exponent and subtract one from the exponent (proof). For example:


The function


can be differentiated as follows:


In graphs, the derivative of a function f at a number a is equal to the slope of the tangent line of the graph of f at the point (a,f(a)) .

See also