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.)

Related Topics:
Mathematics - Calculus - Integral - 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:

Related Topics:
Function - Real

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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 ►