Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Resulting from or employing derivation: a derivative word; a derivative process.
 adj. Copied or adapted from others: a highly derivative prose style.
 n. Something derived.
 n. Linguistics A word formed from another by derivation, such as electricity from electric.
 n. Mathematics The limiting value of the ratio of the change in a function to the corresponding change in its independent variable.
 n. Mathematics The instantaneous rate of change of a function with respect to its variable.
 n. Mathematics The slope of the tangent line to the graph of a function at a given point. Also called differential coefficient, fluxion.
 n. Chemistry A compound derived or obtained from another and containing essential elements of the parent substance.
 n. Business An investment that derives its value from another more fundamental investment, as a commitment to buy a bond for a certain sum on a certain date.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Imitative of the work of someone else.
 adj. Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.
 adj. Having a value that depends on an underlying asset of variable value.
 adj. Lacking originality.
 n. Something derived.
 n. A word that derives from another one.
 n. A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.
 n. A chemical derived from another.
 n. The derived function of a function.
 n. The value of this function for a given value of its independent variable.
from the GNU version of the Collaborative International Dictionary of English
 adj. Obtained by derivation; derived; not radical, original, or fundamental; originating, deduced, or formed from something else; secondary
 adj. Hence, unoriginal (said of art or other intellectual products.
 n. That which is derived; anything obtained or deduced from another.
 n. 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.
 n. 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.
 n. An agent which is adapted to produce a derivation (in the medical sense).
 n. A derived function; a function obtained from a given function by a certain algebraic process.
 n. A substance so related to another substance by modification or partial substitution as to be regarded as derived from it
from The Century Dictionary and Cyclopedia
 Derived; taken or having proceeded from another or something preceding; secondary: as, a derivative word; a derivative conveyance.
 In biology, relating to derivation, or to the doctrine of derivation: as, the derivative theory.
 In medicine, having a tendency to lessen inflammation or reduce a morbid process.
 n. 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. That which is derived; that which is deduced or comes by derivation from another.
 n. 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. In music: The root or generator from which a chord is derived.
 n. Same as derivative chord (which see, above).
 n. In mathematics: A derivative function; a differential coefficient.
 n. 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. More generally, any function derived from another.
 In geology, derived from some other source; not native to the rock in which it is now found.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. resulting from or employing derivation
 n. a compound obtained from, or regarded as derived from, another compound
 n. (linguistics) a word that is derived from another word
 n. a financial instrument whose value is based on another security
 n. the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

The term derivative product is a general term for a contractual agreement between two parties whereby the counterparties exchange  or swap  payments based some underlying benchmarks, applied against a contract notional amount.
David Paul: Credit Default Swaps, the Collapse of AIG and Addressing the Crisis of Confidence

Frodo Baggins is renamed Frodo Sumkin (a derivative from the Russian word sumka, or bag).

Financial markets use the term derivative to describe a transaction that derives its value from an independent reference asset.

This Shuttle C derivative is nothing but a stalking horse to make Ares I/V look better.
Today's Video: NASA Shuttlederived Sidemount Heavy Launch Vehicle Concept  NASA Watch

Dennis, wherever he learned it, derivative is definitely the right word.

(A derivative is an investment whose value comes from, or "derives," from another investment, like stocks, credit, or home mortgages ...)
$1.144 Quadrillion  Total Size Of Derivatives Bubble  The Consumerist

Let the people who traded in derivative drown in the cesspool they created.

Now a story or movie being derivative is not necessarily a bad thing.

Some local governments absorbed huge losses in derivative investments.

I remember a bunch of years ago there was federal legislation pending a Senate vote haviong to do with amendments to either the '33 0r' 34 Securities Act or Securities and Exchange Act, which would have increased the difficulty for plaintiffs in derivative actions and in actions against broker dealers.
Chaching! Health care reform means juicy campaign contributions (Jack Bog's Blog)
ruzuzu commented on the word derivative
"4. 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."
Century Dictionary
April 7, 2011