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. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable.
The concept of a derivative can be extended to many other settings. The common thread is that the derivative of a function at a point serves as a linear approximation of the function at that point.
In finance, a derivative is a type of financial contract whose value is dependent on an underlying asset, group of assets, or benchmark. Derivatives are usually leveraged instruments, which increases their potential risks and rewards. Common derivatives include futures contracts, forwards, options, and swaps.
To calculate a derivative, the process of finding a derivative is called "differentiation". The derivative of a function can be found using derivative rules, which are a set of formulas that allow us to find the derivative of a wide range of functions. The derivative of a function can also be found using the definition of the derivative, which involves taking the limit of the difference quotient as the change in the input approaches zero.
