# What is derivative?

• (adj): Resulting from or employing derivation.
Example: "A derivative process"; "a highly derivative prose style"

## 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.

### 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 ...
Aesculetin
... 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 ...
Logrithm - Analytic Properties - Derivative and Antiderivative
... 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 ...
Proof of Liouville's Formula
... 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) ...
Cannabinoid Receptor Antagonist - Drug Design - Other Derivatives
... 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): 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)