## Derivative

In calculus, a branch of mathematics, the **derivative** is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.

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### Some articles on derivative:

**Derivative**- Generalizations

... The concept of a

**derivative**can be extended to many other settings ... The common thread is that the

**derivative**of a function at a point serves as a linear approximation of the function at that point ... An important generalization of the

**derivative**concerns complex functions of complex variables, such as functions from (a domain in) the complex numbers C to C ...

... and cichorigenin) is a

**derivative**of coumarin ... the intramolecular cyclization of a cinnamic acid

**derivative**... The sodium salt of its methyl-

**derivative**is used in dermatology for the treatment of varicose veins ...

**Derivative**and Anti

**derivative**

... Moreover, as the

**derivative**of f(x) evaluates to ln(b)bx by the properties of the exponential function, the chain rule implies that the

**derivative**of logb(x) is given by That is, the ... In particular, the

**derivative**of ln(x) is 1/x, which implies that the antiderivative of 1/x is ln(x) + C ... The

**derivative**with a generalised functional argument f(x) is The quotient at the right hand side is called the logarithmic

**derivative**of f ...

... By the Leibniz formula for determinants, the

**derivative**of the determinant of Φ = (Φi, j )i, j ∈ {0...n} can be calculated by differentiating one row at a time and taking the sum ... It remains to show that this representation of the

**derivative**implies Liouville's formula ... both sides, using the product rule, the chain rule, the

**derivative**of the exponential function and the fundamental theorem of calculus, we obtain due to the

**derivative**in (3) ...

**Derivative**s

... A large number of fused bicyclic

**derivatives**of diaryl-pyrazole and imidazoles have been reported ... An example of these is a purine

**derivative**where a pyrimidine ring is fused to an imidazole ring ... Otenabant (CP-945,598) is an example of a fused bicyclic

**derivative**developed by Pfizer ...

### More definitions of "derivative":

- (
*noun*): The result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx.

Synonyms: derived function, differential coefficient, differential, first derivative

- (
*noun*): A financial instrument whose value is based on another security.

Synonyms: derivative instrument

- (
*noun*): (linguistics) a word that is derived from another word.

Example:*"'electricity' is a derivative of 'electric'"*

### Famous quotes containing the word derivative:

“When we say “science” we can either mean any manipulation of the inventive and organizing power of the human intellect: or we can mean such an extremely different thing as the religion of science the vulgarized *derivative* from this pure activity manipulated by a sort of priestcraft into a great religious and political weapon.”

—Wyndham Lewis (1882–1957)

“Poor John Field!—I trust he does not read this, unless he will improve by it,—thinking to live by some *derivative* old-country mode in this primitive new country.... With his horizon all his own, yet he a poor man, born to be poor, with his inherited Irish poverty or poor life, his Adam’s grandmother and boggy ways, not to rise in this world, he nor his posterity, till their wading webbed bog-trotting feet get talaria to their heels.”

—Henry David Thoreau (1817–1862)