The common feature of these examples is that they are expressions of the idea that the derivative is part of a functor.

* hedge or mitigate risk in the underlying, by entering into a derivative contract whose value moves in the opposite direction to their underlying position and cancels part or all of it out ;

In the context of the age and period it held the meaning of seeking or forming part of a cultural entity, that of iudea, the Greek derivative of Persian Yehud, and can be compared with hellenismos, meaning acceptance of Hellenic cultural norms ( the conflict between iudaismos and hellenismos lay behind the Maccabeean revolt and hence the invention of the term iudaismos ).

Thus, the derivative of f ( x ) becomes for an infinitesimal, where st (·) denotes the standard part function, which associates to every finite hyperreal the unique real infinitely close to it.

For example, part of the Book of Breathings, a derivative of the Book of the Dead, was a means to ensure the survival of the name.

Since the derivative of ln x is 1 / x, we make ( ln x ) part of u ; since the antiderivative of 1 / x < sup > 2 </ sup > is − 1 / x, we make ( 1 / x < sup > 2 </ sup >) part of v. The formula now yields:

Its terms are represented by the knots, while the threads connecting the latter correspond, in part, to the definitions and, in part, to the fundamental and derivative hypotheses included in the theory.

As part of this work he developed the Gall orthographic projection, a derivative of the Lambert Cylindrical Equal-Area, to project the celestial sphere onto flat paper in a manner that avoided distorting the shapes of the constellations.

The former assumption interprets individual, group and official action as part of a single system and reduces politics and governmental policies to a derivative of three basic analytical terms: society, culture and personality.

This is in large part because they are an Appell sequence, i. e. a Sheffer sequence for the ordinary derivative operator.

One such example of a derivative of this is Shobac, in the name of Christian Shoubach, whom like Johann Rieser, now Risser, was granted a 300 acre land as part of the Lower LaHave region.

The root of the word is meaning " to permit "; another derivative of this word is, The program involved implementing a Turkish adhan program as part of its goals, as opposed to the conventional Arabic call to prayer.

In addition, integration of the area between the zero curve and the first derivative is a measure of the specific heat of that part of the solidification which can lead to rough estimates of the percent volume of a phase.

" Chalfonts " is one of many variations of Cockney rhyming slang for piles, this is derived from Chalfont St Giles but, as is typical with Cockney rhyming slang, the part of the phrase which rhymes with the derivative is omitted.

The name ' hackney ' was once thought to be an anglicized derivative of French haquenée — a horse of medium size recommended for lady riders ; however, current opinion is that it is derived from the village name Hackney ( now part of London ).

The first radial derivative of the radial part of a Slater-type orbital is

From the point of view of modern infinitesimal theory, is an infinitesimal x-increment, is the corresponding y-increment, and the derivative is the standard part of the infinitesimal ratio:

By the 1980s, microprocessors had developed sufficiently for British Rail to carry out pilot trials on existing European ' off the shelf ' ATP – fitting part of the Great Western Main Line with the TBL1 system from ACEC and the Chiltern Main Line route with SELCAB a derivative of the German LZB system from Alcatel and GEC.

It splits into a tangent part and a normal part to the submanifold:, and the tangent part is then the usual derivative in ( see Gauss equation in the Gauss-Codazzi equations ).

It is a derivative of the Old English pre 7th century personal name ' Myrige ', meaning merry, which in the medieval period became a nickname surname given either to a person of ' honest ' character, or a professional clown, one who took part in the theatres of the day.

The minimum total potential energy is found by taking the derivative with respect to H and equating to zero.

Countries where ASL or a derivative of ASL is the national or a widespread language include Barbados, Belize, Benin, Bolivia, Botswana ( with BSL ), Burkina Faso, Burundi, Cameroon, Canada, the Central African Republic, Chad, Côte d ' Ivoire, the Democratic Republic of the Congo, the Dominican Republic, El Salvador, Gabon, Gambia, Ghana, Guinea, Guyana, Haiti, Honduras, Jamaica, Kenya ( minority use ), Liberia, Madagascar ( minority use ), Mali, Mauritania, Niger, Nigeria, Philippines ( L2 use ), Puerto Rico, Senegal, Sierra Leone, Trinidad and Tobago, Togo, and Zimbabwe ( with ZSL ).

Dante concludes ( Paradiso XXVI ) that Hebrew is a derivative of the language of Adam.

Today, his descendants can be found in many places outside of Afghanistan, such as in America, France, Germany, and even in Scandinavian countries such as Denmark and carry the surname of Ziyaee, which is itself a derivative of the King's title.

* Conservation of Momentum: This equation applies Newton's second law of motion to a continuum, whereby force is equal to the time derivative of momentum.

The expression on the left side is a material derivative.

of a function f is a differentiable function F whose derivative is equal to f, i. e., F ′ = f. The process of solving for antiderivatives is called antidifferentiation ( or indefinite integration ) and its opposite operation is called differentiation, which is the process of finding a derivative.

As the derivative of a constant is zero, x < sup > 2 </ sup > will have an infinite number of antiderivatives ; such as ( x < sup > 3 </ sup >/ 3 ) + 0, ( x < sup > 3 </ sup >/ 3 ) + 7, ( x < sup > 3 </ sup >/ 3 ) − 42, ( x < sup > 3 </ sup >/ 3 ) + 293 etc.

The constant is the initial velocity term that would be lost upon taking the derivative of velocity because the derivative of a constant term is zero.

The time derivative of angular momentum is called torque:

The torque caused by the two opposing forces F < sub > g </ sub > and-F < sub > g </ sub > causes a change in the angular momentum L in the direction of that torque ( since torque is the time derivative of angular momentum ).

* Tofisopam ( Emandaxin and Grandaxin ) is a drug that is a benzodiazepine derivative.

Physics is particularly concerned with the way quantities change and evolve over time, and the concept of the " time derivative " — the rate of change over time — is essential for the precise definition of several important concepts.

Legal scholars are concerned that just as technology eases the process of cheaply making and distributing derivative works imbued with new cultural meanings available to wide public, copyright and right-to-publicity law is clamping down on and limiting these works, thus reducing their promulgation, and limiting semiotic democracy.

These directives implied precise emphasis on: the search for political coordination with emerging and developing countries, namely India, South Africa, Russia and China ; creation of the Union of South American Nations and its derivative bodies, such as the South American Security Council ; strengthening of Mercosul ; projection at the Doha Round and WTO ; maintenance of relations with developed countries, including the United States ; undertaking and narrowing of relations with African countries ; campaign for the reform of the United Nations Security Council and for a permanent seat for Brazil ; and defense of social objectives allowing for a greater equilibrium between the States and populations.

* Cone tracing, a derivative of the ray-tracing algorithm that replaces rays, which have no thickness, with cones

In the Lagrangian description, the material derivative of is simply the partial derivative with respect to time, and the position vector is held constant as it does not change with time.

A stationary point is a geometry such that the derivative of the energy with respect to all displacements of the nuclei is zero.

To take the derivative of a composite of more than two functions, notice that the composite of f, g, and h ( in that order ) is the composite of f with.

To compute the derivative of 1 / g ( x ), notice that it is the composite of g with the reciprocal function, that is, the function that sends x to 1 / x.

The derivative of x is the constant function with value 1, and the derivative of f ( g ( x )) is determined by the chain rule.

One proof of the chain rule begins with the definition of the derivative:

One of these, Itō's lemma, expresses the composite of an Itō process ( or more generally a semimartingale ) dX < sub > t </ sub > with a twice-differentiable function f. In Itō's lemma, the derivative of the composite function depends not only on dX < sub > t </ sub > and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way.

Regardless when and by what route it reached England and the British colonies in its recognizable form, croquet is, like pall mall, trucco, jeu de mail and kolven, clearly a derivative of ground billiards, which was popular in Western Europe back to at least the 14th century, with roots in classical antiquity.

The present IUPAC definition is that affinity A is the negative partial derivative of Gibbs free energy G with respect to extent of reaction ξ at constant pressure and temperature.

: denotes the partial derivative of with respect to evaluated for

: denotes the partial derivative of with respect to evaluated for.