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It the rate at which a variable or a function or  a quantity changes with respect to another quantity.

A derivative of a variable y with respect to a variable x means the rate of change of quantity y divided by rate of change in quantity x.

It is the limit to which the change in quantity y divided by the change in quantity x reaches, when the change is quantity x is made arbitrarily small.

\frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}
Nounplural noun: derivatives1.something which is based on another source."the aircraft is a derivative of the Falcon 20G"2.FINANCEan arrangement or product (such as a future, option, or warrant) whose value derives from and is dependent on the value of an underlying asset, such as a commodity, currency, or security."the derivatives market"