# derivative

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**derivative of a function**— the limit if it exists of the quotient of an increment of a dependent variable to the corresponding increment of an associated independent variable as the latter increment tends to zero without being zero …122

**Covariant derivative**— In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …123

**Generalizations of the derivative**— The derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, and geometry. Contents 1 Derivatives in analysis 1.1 Multivariable… …124

**Lie derivative**— In mathematics, the Lie derivative, named after Sophus Lie by Władysław Ślebodziński, evaluates the change of one vector field along the flow of another vector field.The Lie derivative is a derivation on the algebra of tensor fields over a… …125

**Material derivative**— The material derivative[1][2] is a derivative taken along a path moving with velocity v, and is often used in fluid mechanics and classical mechanics. It describes the time rate of change of some quantity (such as heat or momentum) by following… …126

**Total derivative**— In the mathematical field of differential calculus, the term total derivative has a number of closely related meanings. * The total derivative of a function, f , of several variables, e.g., t , x , y , etc., with respect to one of its input… …127

**Fréchet derivative**— In mathematics, the Fréchet derivative is a derivative defined on Banach spaces. Named after Maurice Fréchet, it is commonly used to formalize the concept of the functional derivative used widely in mathematical analysis, especially functional… …128

**Credit derivative**— In finance, a credit derivative is a securitized derivative whose value is derived from the credit risk on an underlying bond, loan or any other financial asset. In this way, the credit risk is on an entity other than the counterparties to the… …