mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical...

analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle {\frac {f'}{f}}} where f ′ {\displaystyle f'} is the derivative...

continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that...

Generalization of the concept of directional derivative Generalizations of the derivative – Fundamental construction of differential calculus Total derivative – Type...

The Fréchet derivative should be contrasted to the more general Gateaux derivative which is a generalization of the classical directional derivative....

differential geometry, the Lie derivative (/liː/ LEE), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including...

In mathematics, the Gateaux differential or Gateaux derivative is a generalization of the concept of directional derivative in differential calculus....

manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was...

scheme Density point Generalizations of the derivative Symmetrically continuous function Peter R. Mercer (2014). More Calculus of a Single Variable. Springer...

This generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is...

at which the slope of the tangent line is zero. Such a point is known as a stationary point. It is a point at which the first derivative of the function...

derivative – Derivative defined on normed spaces Gateaux derivative – Generalization of the concept of directional derivative Generalizations of the derivative –...

generally give a better approximation of the derivative and examples of such filters are Gaussian derivatives and Gabor filters. Sometimes high frequency...

mathematics, in the area of combinatorics and quantum calculus, the q-derivative, or Jackson derivative, is a q-analog of the ordinary derivative, introduced...

In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable...

called the Radon–Nikodym derivative. The choice of notation and the name of the function reflects the fact that the function is analogous to a derivative in...

the concept of directional derivative Generalizations of the derivative – Fundamental construction of differential calculus Gradient#Total derivative –...

{v} )} . The gradient admits multiple generalizations to more general functions on manifolds; see § Generalizations. Consider a room where the temperature...

{\displaystyle {\dot {y}}} are understood to be functions of t. Generalizations of the derivative Derivative for parametric form at PlanetMath. Harris, John W...

space, in which those generalizations are the Gateaux derivative and the Fréchet derivative. One deficiency of the classical derivative is that very many...

motivation for this concept is the fact that Leibniz-additive functions are generalizations of the arithmetic derivative D {\displaystyle D} ; namely,...

specifically, real analysis, the Dini derivatives (or Dini derivates) are a class of generalizations of the derivative. They were introduced by Ulisse...

mathematics, the Clarke generalized derivatives are types generalized of derivatives that allow for the differentiation of nonsmooth functions. The Clarke derivatives...

mathematics, the quasi-derivative is one of several generalizations of the derivative of a function between two Banach spaces. The quasi-derivative is a slightly...

more natural generalization of the single-variable derivative. It allows a generalization of the single-variable fundamental theorem of calculus to higher...

products). The generalization of grad and div, and how curl may be generalized is elaborated at Curl § Generalizations; in brief, the curl of a vector field...

the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of...

time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable...

analysis, the fractal derivative or Hausdorff derivative is a non-Newtonian generalization of the derivative dealing with the measurement of fractals,...

In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus. Let i : H → E {\displaystyle...