In mathematics, a derivative is a fundamental tool of calculus that shows the sensitivity of change of a functions output with respect to the input. It is the instantaneous rate of change of a function at a particular point. The derivative of a function f is denoted by f and is defined as the limit of the difference quotient as the change in the input approaches zero. The derivative of a function can be used to find the slope of the tangent line to the graph of the function at a particular point. The concept of a derivative can be extended to many other settings, such as complex functions of complex variables.

In finance, a derivative is a contract between two or more parties whose value is dependent on one or more underlying assets. The most common types of derivatives are futures, options, forwards, and swaps. Derivatives are used to access specific markets and trade different assets, and they are considered a form of advanced investing. The value of a derivative is determined by fluctuations in the underlying asset.

In summary, a derivative is a term used in both mathematics and finance, but with different meanings. In mathematics, it is a tool of calculus that shows the instantaneous rate of change of a function at a particular point, while in finance, it is a contract whose value is dependent on one or more underlying assets.