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Derivative

See Derivative (disambiguation) for alternate meanings.

Topics in Calculus

Fundamental theorem | Function | Limits of functions | Continuity | Calculus with polynomials

Differentiation

Product rule | Quotient rule | Chain rule | Implicit differentiation | Taylor's theorem

Integration

Integration by substitution | Integration by parts | Integration by trigonometric substitution | Solids of revolution | Integration by disks | Integration by cylindrical shells | Lists of integrals

Vector Calculus

Vector | Vector field | Matrix | Partial Derivative | Gradient | Flux | Divergence | Divergence Theorem | Del | Curl | Stokes' Theorem

In mathematics, the derivative of a function is one of the two central concepts of calculus. The inverse of a derivative is called the antiderivative, or indefinite integral.
The derivative of a function at a certain point is a measure of the rate at which that function is changing as an argument undergoes change. That is, a derivative embodies in terms of mathematics a rate of change. A derivative is the computation of the instantaneous slopes of f(x) at every point x. This corresponds to the slopes of the tangents to the graph of said function at said point; the slopes of such tangents can be approximated by a secant. Derivatives can also be used to compute concavity.
Functions do not have derivatives at points where they have either a vertical tangent or a discontinuity.