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Except Finance "Derivatives" is used in Mathematics(Calculus) & Chemistry also.

In finance, a derivative is a financial contract with a value linked to the expected future price movements of the asset it is linked to - such as a share or a currency. There are many kinds of derivatives, with the most notable being swaps, futures, and options. However, since a derivative can be placed on any sort of security, the scope of all derivatives possible is near endless. Thus, the real definition of a derivative is an agreement between two parties that is contingent on a future outcome.

A common misconception is to refer to derivatives as assets. This is erroneous, since a derivative is incapable of having value of its own. However, some more commonplace derivatives, such as swaps, futures, and options, which have a theoretical face value that can be calculated using formulas, such as Black-Scholes, are frequently traded on open markets before their expiration date as if they were assets.

Derivatives are usually broadly categorized by the:

relationship between the underlying and the derivative (e.g., forward, option, swap)
type of underlying (e.g., equity derivatives, foreign exchange derivatives, interest rate derivatives, commodity derivatives or credit derivatives)
market in which they trade (e.g., exchange-traded or over-the-counter)
pay-off profile (Some derivatives have non-linear payoff diagrams due to embedded optionality)

Source:Wikipedia