# derivative

## Definitions

• WordNet 3.6
• adj derivative resulting from or employing derivation "a derivative process","a highly derivative prose style"
• n derivative the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
• n derivative (linguistics) a word that is derived from another word "electricity' is a derivative of electric'"
• n derivative a financial instrument whose value is based on another security
• n derivative a compound obtained from, or regarded as derived from, another compound
• ***
Webster's Revised Unabridged Dictionary
• Interesting fact: Leather skin does not have any smell. The leather smell that you sense is actually derived from the materials used in the tanning process
• Derivative Hence, unoriginal (said of art or other intellectual products.
• Derivative (Mus) A chord, not fundamental, but obtained from another by inversion; or, vice versa, a ground tone or root implied in its harmonics in an actual chord.
• Derivative (Math) A derived function; a function obtained from a given function by a certain algebraic process.
• Derivative (Chem) A substance so related to another substance by modification or partial substitution as to be regarded as derived from it; thus, the amido compounds are derivatives of ammonia, and the hydrocarbons are derivatives of methane, benzene, etc.
• Derivative (Gram) A word formed from another word, by a prefix or suffix, an internal modification, or some other change; a word which takes its origin from a root.
• Derivative (Med) An agent which is adapted to produce a derivation (in the medical sense).
• a Derivative Obtained by derivation; derived; not radical, original, or fundamental; originating, deduced, or formed from something else; secondary; as, a derivative conveyance; a derivative word.
• Derivative That which is derived; anything obtained or deduced from another.
• ***
Century Dictionary and Cyclopedia
• Interesting fact: The word "umbrella" is derived from the Latin root word "umbra", which means shade or shadow
• derivative Derived; taken or having proceeded from another or something preceding; secondary: as, a derivative word; a derivative conveyance.
• derivative In biology, relating to derivation, or to the doctrine of derivation: as, the derivative theory.
• derivative In medicine, having a tendency to lessen inflammation or reduce a morbid process.
• n derivative In medicine, a therapeutic method or agent employed to lessen a morbid process in one part by producing a flow of blood or lymph to another part, as cupping, leeching, blisters, catharsis, etc.
• n derivative That which is derived; that which is deduced or comes by derivation from another.
• n derivative Specifically A word derived or formed either immediately from another, or remotely from a primitive or root: thus, ‘verb,’ ‘verbal,’ ‘verbose’ are derivatives of the Latin verbum; ‘duke,’ ‘duct,’ ‘adduce,’ ‘conduce,’ ‘conduct,’ ‘conduit,’ etc., are derivatives of the Latin ducere; ‘feeder’ is a derivative of ‘feed,’ and ‘feed’ a derivative of ‘food.’ See derivation, 3.
• n derivative In music: The root or generator from which a chord is derived.
• n derivative Same as derivative chord (which see, above).
• n derivative In mathematics: A derivative function; a differential coefficient.
• n derivative The slope of a scalar function; a vector function whose direction is that of most rapid increase of a scalar function (of which it is said to be the derivative), and whose magnitude is equal to the increase in this direction of the scalar function per unit of distance
• n derivative More generally, any function derived from another.
• derivative In geology, derived from some other source; not native to the rock in which it is now found.
• ***
Chambers's Twentieth Century Dictionary
• Interesting fact: The word vaccine comes from the Latin word "vacca," which means cow. This name was chosen beacause the first vaccination was derived from cowpox which was given to a boy
• adj Derivative derived or taken from something else: not radical or original
• ***

## Quotations

• Jean Jacques Rousseau
“Adversity is a great teacher, but this teacher makes us pay dearly for its instruction; and often the profit we derive, is not worth the price we paid.”
• Henry Fielding
“It is not from nature, but from education and habits, that our wants are chiefly derived.”
• Confucius
“The strength of a nation derives from the integrity of the home.”
• Eric Hoffer
“The pleasure we derive from doing favors is partly in the feeling it gives us that we are not altogether worthless. It is a pleasant surprise to ourselves.”
• E. M. Cioran
“Every thought derives from a thwarted sensation.”
• Holly Ketchel
“My happiness derives from knowing the people I love are happy.”

## Etymology

Webster's Revised Unabridged Dictionary
L. derivativus,: cf. F. dérivatif,
Chambers's Twentieth Century Dictionary
O. Fr. deriver—L. derivārede, down from, rivus, a river.

## Usage

### In literature:

All governments derive their powers from the consent of the governed.
"Children of the Market Place" by Edgar Lee Masters
Some of them are extremely remote and derivative.
"Falling in Love" by Grant Allen
In what way did the North derive advantages from slavery?
"History of the United States" by Charles A. Beard and Mary R. Beard
The glory that he would derive from their unhappiness can be nothing but a false glory.
"Theodicy" by G. W. Leibniz
The Ghateen derive their subsistence almost entirely from the caravans, although their little oasis is not unfertile.
"Narrative of a Mission to Central Africa Performed in the Years 1850-51, Volume 1" by James Richardson
They are said to derive valuable hints from you, particularly in their management of the pathetic.
"Punch, or the London Charivari, Volume 1, Complete" by Various
This is an important paper, and contains notices of several new stocks, derived from a study of the material furnished by Powers.
"Indian Linguistic Families Of America, North Of Mexico" by John Wesley Powell
All their ideas are derived from things as presented to their observations.
"Lectures on Language" by William S. Balch
After the remarks to which I had been an unwilling listener, I derived very little pleasure from the party.
"The Path of Duty, and Other Stories" by H. S. Caswell
And where does Congress derive the power to pass laws to punish offenders against the laws of a State?
"An Account of the Proceedings on the Trial of Susan B. Anthony" by Anonymous
The word hygiene is derived from Hygeia, the name of the Greek goddess of health.
"The People's Common Sense Medical Adviser in Plain English" by R. V. Pierce
I know whence my ideas of human nature were derived.
"Arthur Mervyn" by Charles Brockden Brown
The interest of the life of Cassiodorus is derived from his position rather than from his character.
"The Letters of Cassiodorus" by Cassiodorus (AKA Magnus Aurelius Cassiodorus Senator)
But the real importance of the affair was derived from its operation on the spirits of the whole army.
"The Life of George Washington, Vol. 2 (of 5)" by John Marshall
But let us not overlook the fact that many recognized experiences testify to the derivation of dreams from the somatic stimulus.
"A General Introduction to Psychoanalysis" by Sigmund Freud
For these reasons we think that no part of the Post Office revenue was derived from the letting of post-horses.
"The History of the Post Office" by Herbert Joyce
The vagina normally secretes a thin opalescent acid fluid derived from the lymph serum and the shedding of squamous epithelium.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 7" by Various
The revenue derived from taxes and customs is about L80,000.
"Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 1" by Various
The English form follows the Romance analogy, possibly because derived directly from France.
"Encyclopaedia Britannica, 11th Edition, Volume 15, Slice 4" by Various
They state that the mesoblast is entirely derived from the formative cells.
"The Works of Francis Maitland Balfour, Volume 1" by Francis Maitland Balfour
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### In poetry:

You that dispose of all our Lives,
Praise him from whom your Pow'r derives:
Be True and Just, like him, and fear his Word,
As much as Malefactors do your Sword.
"A Paraphrase On The CXLVIIIth Psalm" by Wentworth Dillon
O you that were my Beauty and my Own,
Although from you derive all my mischance,
Are not you still my Home, then, you alone,
As young and mad and beautiful as France?
"Birds In The Night" by Paul Verlaine
For like the vapour in the brain,
Derived from sickness, or from pain;
The spirits they did flow amain,
Then homewards he returned again,
With all his speed.
"On The Death Of John Simpson, Castlemilk" by Susannah Hawkins
Hail! venerable, British oak,
Beneath whose shade the Druids spoke:
Deriv'd from thy oraculous tree,
Sprung misseltoe, and prophesy;
And mystic sounds inspir'd by Jove,
Once murmur'd thro' Dodona's grove.
"The Description of a Cottage" by Samuel Bowden
Then ask ye, from what cause on earth
Virtues like these derive their birth?
Derived from Heaven alone,
Full on that favour’d breast they shine,
Where faith and resignation join
To call the blessing down.
"An Ode, On Reading Mr. Richardson's History Of Sir Charles Grandison" by William Cowper
She is like the fair woodbine that wreathes round the oak,
That derives its support from the tree's noble stem ;
And, tho' it be scathed by the lightning's dread stroke,
Still weaves of its flowrets a rich diadem.
"On Reading An Assertion" by Mary Anne Browne

### In news:

In other words, the cached credentials can't be used to derive either the password hash or the original password.
There was the time I purchased Red Rim, derived from the poet's daffodils that see out the season in their bone-white petals and red eyes.
This Cuban drink derives it's name from a town on the island's southeastern coast.
Kat Dennings does her career no favors in derivative drama.
In this instance, it is clear that there is a benefit derived by the corporation from this arrangement.
Ted Frank Upends Sears Derivative Suit in Plaintiffs Lawyer-Bashing Seventh Circuit Ruling.
A Monday report by Reuters said that New York City's pension funds have filed a derivative lawsuit against Wal-Mart Stores Inc based on reported allegations of bribery in Mexico and a possible cover-up by Wal-Mart officials.
This is why JPMorgan Chase's admission Thursday that it had suffered a $2.3 billion loss and an$800 million gouge in its earnings from unmonitored derivatives trading is so distressing.
Fiat to build a 'baby' Jeep, Fiat derivative in Italy.
Sure, but Also Derivative .
DEA Now Monitoring Krokodil, a Deadly Morphine Derivative .
The business office must develop an understanding and inventory of derivatives , and implement the standard this fiscal year.
Hear how the GASB standard applies to management intent, characteristics, and performance of derivatives .
It is derivative 's tendency to act quickly that introduces most of the problems.
Jazz musician and entertainer Louis Armstrong's nickname Satchmo derives from the phrase "satchel mouth," used to describe the New Orleans trumpeter's wide grin and impressive embouchure.
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### In science:

More precisely, the bounded derived category Db (mod-B ) of ﬁnitely generated B -modules, as wel l as the unbounded derived category D(Mod-B ) of al l B -modules, are simple in the sense that they do not admit nontrivial recol lements by derived categories of the same type.
Blocks of group algebras are derived simple
We focus on (bounded or unbounded) derived categories of ﬁnite-dimensional algebras. A derived category is said to be simple if it is nonzero and it is not the middle term of a nontrivial recollement of derived categories.
Blocks of group algebras are derived simple
These symmetries allow the effective theory to be written in terms of Fmn only, and as the result, the Lagrangian can be ordered in powers of derivatives of the photon ﬁeld. A derivative translates int o the momentum, or energy, and hence the derivative expansion translates into the expansion in energy.
Baryon chiral perturbation theory: an update
The most attractive feature of higher derivative theories possessing the Galilean invariance ∂µφ → ∂µφ + bµ is that ﬁeld equations derived from such a theory contain derivatives only up to second order,10) so that it can easily avoid ghosts.
Generalized G-inflation: Inflation with the most general second-order field equations
In this cases we proved that generalized δ -derivation is a generalized derivation or δ -derivation.
Generalized \delta-Derivations
The where H = −∇α [N (δα covariant derivative of uα appears in the action so, although the matter is a scalar ﬁeld, the aether part of E α β has derivatives of order two on gαβ and three on T , while H has derivatives of one higher order on each ﬁeld variable.
Initial value constraints with tensor matter
It is not until the gauge x0 = T is chosen that the time derivative order of the theory drops to two: the ﬁeld variable T disappears from the equations, and the derivative orders of E α β and H remain two and three respectively, but the third derivative in the H ﬁeld equation is always in a spatial direction.
Initial value constraints with tensor matter
Since the norm of the derivative of order k can be bounded (in both directions) by the sum of norms of partial derivatives up to order k (neglecting a constant) it suﬃces to estimate each partial derivative.
Pesin's Formula for Random Dynamical Systems on $R^d$
We will soon use its derivatives in the parameters: the vector of X ε and its ﬁrst derivatives in µ still satisfy a linear system of ODEs whose coeﬃcients depend linearly on the parameters and on the process ν (x/ε2 ), and the same result holds adding higher order derivatives.
Stability of solitons under rapidly oscillating random perturbations of the initial conditions
Another easy computation shows that the curve c is ¯δx -derivable if and only if the curve c is ¯δ -derivable at t = 0, which is true, therefore c is ¯δx -derivable, in particular at t = 0.
Sub-riemannian geometry from intrinsic viewpoint
Whereas initially the temperature structure for i = 1 was derived assuming a time derivative of zero, equivalent to assuming a constant J/ρ over time, these steps need to be iterated until the derivative converges for i = 1.
Radiation Energy-Balance Method for Calculating the Time Evolution of Type Ia Supernovae During the Post-Explosion Phase
Two of the authors had earlier derived an operator sum representation of the SGAD channel, by generalizing the GAD channel. A different derivation, that exploits the Choi channel-state isomorphism was presented here, along with the unitary operation relating it to the previous derivation.
Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry
LX and iX denote exterior derivative, Lie derivative and interior derivative with respect to X , respectively.
Lie Groupoids and Generalized Almost Subtangent Manifolds
Another types of ﬁnite-time future singularities are type II singularity where the second derivative of scale factor becomes inﬁnite at ﬁnite time while the ﬁrst derivative is ﬁnite and type III singularity where the ﬁrst derivative of scale factor diverges.
Confronting dark energy models mimicking $\Lambda$CDM epoch with observational constraints: future cosmological perturbations decay or future Rip?
If the monoid indexing the graded ring structure of B is rather restricted (see Theorem 1.9 below), the derivation D is close to what is called an Euler derivation mixed with a locally nilpotent derivation.
Algebraic derivations on affine domains
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