Derivativ

Derivativ, often spelled derivative, is a term used in mathematics and finance to describe things that come from another quantity. In calculus, the derivative of a function measures its instantaneous rate of change with respect to a variable. If a function f is differentiable at a point x, the derivative f′(x) is defined as the limit of (f(x + h) − f(x)) / h as h approaches zero. The derivative gives the slope of the function’s graph at that point and relates to the differential df = f′(x) dx. Derivatives obey rules such as the chain rule, product rule, and quotient rule, and can be extended to higher orders (second derivative, etc.) to analyze curvature and acceleration.

In finance, a derivative is a contract whose value is derived from the price or other characteristics of an underlying asset, such as a stock, commodity, currency, or index. Common derivatives include futures, forwards, options, and swaps. They are used for hedging risk, speculation, and arbitrage. Pricing depends on factors like the underlying price, time to maturity, volatility, interest rates, and dividends. The name reflects that the instrument’s value is not intrinsic but derived from the underlying asset.

The term appears across languages with similar meanings, and the concept connects across disciplines by focusing on quantities that depend on or originate from other quantities. See calculus derivative and financial derivative for more detailed treatments.