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A delta one product is a derivative with a linear, symmetric payoff profile. That is, a derivative that is not an option or a product with embedded options. Examples of delta one products are Exchange-traded funds, equity swaps, custom baskets, linear certificates, futures, forwards, exchange-traded notes, trackers, and Forward rate agreements ...
In chemistry, a derivative is a compound that is derived from a similar compound by a chemical reaction.. In the past, derivative also meant a compound that can be imagined to arise from another compound, if one atom or group of atoms is replaced with another atom or group of atoms, [1] but modern chemical language now uses the term structural analog for this meaning, thus eliminating ambiguity.
The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. [3] It represents a specialized cursive type of the letter d , just as the integral sign originates as a specialized type of a long s (first used in print by ...
Derivatization is a technique used in chemistry which converts a chemical compound into a product (the reaction's derivate) of similar chemical structure, called a derivative. Generally, a specific functional group of the compound participates in the derivatization reaction and transforms the educt to a derivate of deviating reactivity ...
The generalized Kronecker delta or multi-index Kronecker delta of order is a type (,) tensor that is completely antisymmetric in its upper indices, and also in its lower indices. Two definitions that differ by a factor of p ! {\displaystyle p!} are in use.
A number of properties of the differential follow in a straightforward manner from the corresponding properties of the derivative, partial derivative, and total derivative. These include: [ 11 ] Linearity : For constants a and b and differentiable functions f and g , d ( a f + b g ) = a d f + b d g . {\displaystyle d(af+bg)=a\,df+b\,dg.}
The derivative of the delta function satisfies a number of basic properties, including: [50] ′ = ′ ′ = which can be shown by applying a test function and integrating by parts. The latter of these properties can also be demonstrated by applying distributional derivative definition, Leibniz 's theorem and linearity of inner product: [ 51 ]
The second-derivative test for functions of one and two variables is simpler than the general case. In one variable, the Hessian contains exactly one second derivative; if it is positive, then x {\displaystyle x} is a local minimum, and if it is negative, then x {\displaystyle x} is a local maximum; if it is zero, then the test is inconclusive.