Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation.
In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the underlying. Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation, or getting access to otherwise hard-to-trade assets or markets.
The derivatives market is the financial market for derivatives - financial instruments like futures contracts or options - which are derived from other forms of assets.
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator
Anthracene is a solid polycyclic aromatic hydrocarbon (PAH) of formula C14H10, consisting of three fused benzene rings. It is a component of coal tar. Anthracene is used in the production of the red dye alizarin and other dyes. Anthracene is colorless but exhibits a blue (400–500 nm peak) fluorescence under ultraviolet radiation.
Medroxyprogesterone (MP), is a progestin which is not used medically. A derivative, medroxyprogesterone acetate (MPA), is used as a medication in humans, and is far more widely known in comparison. Medroxyprogesterone is sometimes used as a synonym for medroxyprogesterone acetate, and what is almost always being referred to when the term is used is MPA and not medroxyprogesterone.
Iclazepam (Clazepam) is a drug which is a benzodiazepine derivative. It has sedative and anxiolytic effects similar to those produced by other benzodiazepine derivatives, and is around the same potency as chlordiazepoxide.
IDRA-21 is a positive allosteric modulator of the AMPA receptor and a benzothiadiazine derivative. It is a chiral molecule, with (+)-IDRA-21 being the active form.
In copyright law, a derivative work is an expressive creation that includes major copyrightable elements of a first, previously created original work. The derivative work becomes a second, separate work independent from the first. The transformation, modification or adaptation of the work must be substantial and bear its author's personality sufficiently to be original and thus protected by copyright. Translations, cinematic adaptations and musical arrangements are common types of derivative works.
AMDA (9-Aminomethyl-9,10-dihydroanthracene) is an organic compound which acts as a potent and selective antagonist for the 5-HT2A receptor. It has been used to help study the shape of the 5-HT2A protein, and develop a large family of related derivatives with even higher potency and selectivity.
MT-45 (IC-6) is an opioid analgesic drug invented in the 1970s by Dainippon Pharmaceutical Co. It is chemically a 1-substituted-4-(1,2-diphenylethyl) piperazine derivative, which is structurally unrelated to most other opioid drugs. Racemic MT-45 has around 80% the potency of morphine, with almost all opioid activity residing in the (S) enantiomer. It has been used as a lead compound from which a large family of potent opioid drugs have been developed, including full agonists, partial agonists, and antagonists at the three main opioid receptor subtypes. Fluorinated derivatives of MT-45 such as 2F-MT-45 are significantly more potent as μ-opioid receptor agonists, and one of its main metabolites 1,2-diphenylethylpiperazine also blocks NMDA receptors.
ADBICA (also known as ADB-PICA) is a designer drug identified in synthetic cannabis blends in Japan in 2013. ADBICA had not previously been reported in the scientific literature prior to its sale as a component of synthetic cannabis blends. ADBICA features a carboxamide group at the 3-indole position, like SDB-001 and STS-135. The stereochemistry of the tert-butyl side-chain in the product is unresolved, though in a large series of indazole derivatives structurally similar to ADBICA that are disclosed in Pfizer patent WO 2009/106980, activity resides exclusively in the (S) enantiomers. ADBICA is a potent agonist of the CB1 receptor and CB2 receptor with an EC50 value of 0.69 nM and 1.8 nM respectively.
The substituted benzofurans are a class of chemical compounds based on the heterocyclyc and polycyclic compound benzofuran. Many medicines use the benzofuran core as a scaffold, but most commonly the term is used to refer to the simpler compounds in this class which include numerous psychoactive drugs, including stimulants, psychedelics and empathogens. In general, these compounds have a benzofuran core to which a 2-aminoethyl group is attached, and combined with a range of other substituents. Some psychoactive derivatives from this family have been sold under the name Benzofury.
17α-Methyl-19-norprogesterone, also known as 17α-methyl-19-norpregn-4-ene-3,20-dione, is a progestin which was never marketed. It is a derivative of progesterone, and is the combined derivative of 17α-methylprogesterone and 19-norprogesterone. The drug is the parent compound of a subgroup of the 19-norprogesterone group of progestins, which includes demegestone, promegestone, and trimegestone.
α-PCyP is a stimulant drug of the cathinone class that has been sold online as a designer drug. In a series of alpha-substituted pyrrolidinyl cathinone derivatives developed in 2015, the alpha-cyclopentyl derivative was found to have around the same potency in vitro as an inhibitor of the dopamine transporter as the alpha-propyl derivative α-PVP, while the alpha-cyclohexyl derivative α-PCyP was around twice as strong.
α-Pyrrolidinoisohexanophenone is a stimulant drug of the cathinone class that has been sold online as a designer drug. It is a positional isomer of pyrovalerone, with the methyl group shifted from the 4-position of the aromatic ring to the 4-position of the acyl chain. In a classic 2006 study of pyrrolidinyl cathinone derivatives by Meltzer et al. at Organix, the alpha-isobutyl derivative of pyrovalerone, O-2494, was found to have the highest potency in vitro as an inhibitor of the dopamine transporter of the alpha substituted derivatives tested. α-PiHP acts as a norepinephrine–dopamine reuptake inhibitor. Compared to α-PVP and α-PHP, α-PiHP displays a higher selectivity for the dopamine transporter. Similar to other cathinones, use of α-PiHP can result in compulsive redosing, addiction, anxiety, paranoia, and psychosis. In July 2016 α-PHiP was first identified as a designer drug when it was reported to the EMCDDA by a forensic laboratory in Slovenia.
Bromerguride, also known as 2-bromolisuride, is an antidopaminergic and serotonergic agent of the ergoline group which was described as having atypical antipsychotic properties but was never marketed. It was the first antidopaminergic ergoline derivative to be discovered. The pharmacodynamic actions of bromerguride are said to be "reversed" relative to its parent compound lisuride, a dopaminergic agent.
THC morpholinylbutyrate is a synthetic derivative of tetrahydrocannabinol, developed in the 1970s. It is a prodrug which is converted into THC inside the body, and was one of the first derivatives of THC that is able to form water-soluble salts, giving it a significant advantage over THC for some applications. However, it is less potent than THC and the metabolic conversion to THC is relatively slow and variable, giving it unpredictable pharmacokinetics which has limited its research applications.
