Exterior derivative (5018 bytes)
1: In [[mathematics]], the '''exterior derivative''' operator of [[differential topology]], extends...
6: The exterior derivative of a differential form of degree ''k'' is a diffe...
16: Exterior differentiation satisfies three important propert...
24: ... formula encoding the equality of [[mixed partial derivatives]], so that always
28: It can be shown that exterior derivative is uniquely determined by these properties and it...

Exterior algebra (10539 bytes)
1: ...ation, known as the '''wedge product''' or the '''exterior product''', is written as ∧. The wedge produc...
8: ...s. This means that all equations that hold in the exterior algebra follow from the above properties alone. T...
10: ...d denoted by Λ^''k''(''V''). The exterior algebra can be written as the [[direct sum]] of e...
12: ...an ''l''-vector is a ''k''+''l''-vector. Thus the exterior algebra forms a [[graded algebra]] where the grad...
14: Exterior powers find their main application in [[differen...

Exterior (topology) (382 bytes)
2: ...open set]]s of ''X'' which do not meet ''S''. The exterior of ''S'' is denoted by

Derivative (17963 bytes)
3: ...is the [[antiderivative]], the [[inverse]] of the derivative.)
5: ...etrical interpretation, it is not surprising that derivatives can be used to determine many geometrical prop...
7: ...ontinuity]]. However, functions may fail to have derivatives even if they are continuous and have no vertical...
15: ...roaches 0. In [[Leibniz|Leibniz]]'s notation, the derivative of ''y'' with respect to ''x'' is written
25: ...in more detail below. If ''f'' is a function, the derivative of the function ''f'' at the value ''x'' is writt...

Exterior Gateway Protocol (681 bytes)
1: The '''Exterior Gateway Protocol''' ('''EGP''') is a [[routing pr...
3: During the early days of the Internet, an Exterior Gateway Protocol, EGP version 3, was used to inte...

Convective derivative (1050 bytes)
1: ... known as the '''Lagrangian derivative''', is a [[derivative]] taken with a respect to a [[coordinate system]]...
7: ...to t. Proof is via the [[chain rule]] for partial derivatives.
9: ...e following identities when taking the convective derivative of an [[integral]]:

Schwarzian derivative (1133 bytes)
1: In [[mathematics]], the '''Schwarzian derivative''' of a function of one [[complex variable]] <mat...
5: The Schwarzian derivative of a [[linear fractional transformation]]
11: ...ion <math>g\circ f</math> has the same Schwarzian derivative as <math>f</math>.
13: On the other hand the Schwarzian derivative of <math>f\circ g</math>, where <math>g</math> is...
18: ...approximated by a linear function, the Schwarzian derivative tells us how a function can be approximated by a ...

Freight derivative (755 bytes)
1: ...to be traded on ''BIFFEX'' and ''INTEX''. Freight derivatives are primarily used by shipowners and operators, ...
3: [[Category:Derivatives]]

Substantive derivative (1515 bytes)
1: ...ive''', '''material derivative''' or '''advective derivative'''), written <math>D/Dt</math>, is the [[rate of ...
3: ... small parcel, hence the other names '''advective derivative''' and
4: '''fluid following derivative'''.
12: ...pare the substantive derivative with the Eulerian derivative (written <math>\partial/\partial t</math>) in whi...
14: ... velocity is everywhere zero, but the substantive derivative is nonzero because any individual parcel of fluid...

First derivative test (2025 bytes)
1: ...ulus]], a branch of [[mathematics]], the '''first derivative test''' determines whether a given [[stationary p...
5: ...is negative, then ''f'' is decreasing. The first derivative test now states:

Second derivative test (1280 bytes)
1: ...stationary point]] of a function (where its first derivative is zero) is a [[maximum]], a [[minimum]], or neit...
3: ...on on the first derivative in terms of the second derivative. Suppose that ''f'' is twice [[differentiable]] ...

Total derivative (979 bytes)
1: ...be used compatibly (ii) to express the [[exterior derivative]] ''d'', as applied to [[differential form]]s, an...
5: where ''F''_''i'' is the partial derivative with respect to ''x''_''i''.
7: ...in terms of total derivatives. Since the exterior derivative is a [[natural operator]], in a sense that can be...

Derivative algebra (533 bytes)
3: ...tructure]] that provides an abstraction of the '''derivative operator''' in [[topological space|topology]] and...
5: * In [[differential geometry]] a '''derivative algebra''' is a [[vector space]] with a product o...

Halogen derivative (418 bytes)
1: ...situted for [[hydrogen]] atoms. In naming halogen derivatives, the suffix of the halogen is changed to ''-o'' ...

Derivative (disambiguation) (682 bytes)
1: Generally, a '''derivative''' is a thing that is based on, or created from, ...
3: ...nt of derivatives in differential calculus, see [[derivative]].
4: *In [[linguistics]] and [[etymology]], a '''derivative''' is a word that is formed from a more basic wor...
5: *In [[chemistry]] a '''derivative''' is a [[chemical compound|compound]] that is fo...
6: *[[Derivative security]], for an account of derivatives in [[finance]]

Derivative work (3219 bytes)
3: ... non-trivial copyrighted material is called a "'''derivative work'''."
5: A derivative work may be a [[translation]], [[musical arrangem...
7: ...exercised considerable control over any potential derivative works, including (but not limited to) banning the...
9: ... the original work and its reused elements in the derivative are always retained by the original author.
13: ...non-trivial" [[copyrighted material]], and thus a derivative work, is a question that keeps many copyright [[l...

Covariant derivative (11275 bytes)
1: ...ovariant derivative''' is a way of specifying a [[derivative]] along [[vector field]]s on a manifold.
3: There is no real difference between the covariant derivative and the [[Connection (mathematics)|connection]] c...
5: ...[pseudo-Riemannian manifold]]s the term covariant derivative is often used for the [[Levi-Civita connection]].
7: ...with respect to a [[vector field]]; the covariant derivative of a [[tensor]] is an extension of the same conce...
13: ...te system). Upon fixing a coordinate system, this derivative transforms under a change of coordinates "in the ...

Derivative of a constant (1487 bytes)
1: In [[calculus]], the [[derivative]] of a [[constant]] [[function (mathematics)|func...
3: ...natively, one can use the limit definition of the derivative.
5: ==Consequences for antiderivatives==
7: ...e the same derivative; so that in taking an [[antiderivative]] there is the indeterminacy of adding any consta...
9: ...he derivative of a constant. Which is 0: the anti-derivative of ''x''^-1 can't be a polynomial

Pincherle derivative (1080 bytes)
1: In [[mathematics]], the '''Pincherle derivative''' of a [[linear operator]] ''T'' on the space of...
15: ... this form, then it is easy to find its Pincherle derivative in this form, by using the fact that

Derivative (examples) (1981 bytes)
6: The derivative of a [[constant]] is [[zero]].
17: The derivative and slope are equivalent.

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