Derivative

In mathematics, the derivative is one of the two central concepts of calculus. (The other is the integral; the two are related via the fundamental theorem of calculus.)

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The simplest type of derivative is the derivative of a real-valued function of a single real variable. It has several interpretations:

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• The derivative gives the slope of a tangent to the graph of the function at a point. In this way, derivatives can be used to determine many geometrical properties of the graph, such as concavity or convexity.
• The derivative provides a mathematical formulation of rate of change; it measures the rate at which the function's value changes as the function's argument changes.

This derivative is the kind usually encountered in a first course on calculus, and historically was the first to be discovered. However, there are also many generalizations of the derivative.

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The remainder of this article discusses only the simplest case (real-valued functions of real numbers).

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Derivative: Differentiation and differentiability ►



 

Calculus: :For other uses of the term calculus see calculus (disambiguation)...

Integral: : This article deals with the concept of an integral in calculus. For other meanings of "integral" see integration and integral (disambiguation)....

Fundamental theorem of calculus: The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverses of each other. This means that if a continuous function is first integrated and then differentiated, the original function is retrieved. This theorem is of ...