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 and the slope of the tangent line to the graph of the function at a chosen input value. The derivative of a function of a single variable at a chosen input value, when it exists, is the best linear approximation of the function near that input value. The concept of a derivative can be extended to many other settings, and 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 financial contracts set between two or more parties, and traders use them to access specific markets and trade different assets. The most common underlying assets for derivatives include stocks, bonds, commodities, currencies, and interest rates. Derivatives are usually leveraged instruments, which increases their potential risks and rewards.
To find the derivative of a function, we use the slope formula, which is the change in Y over the change in X. The derivative of a function is commonly written as d/dx of f(x) or f(x). The derivative of a function can be calculated using various notations, such as Leibnizs, Lagranges, and Newtons notations.
In summary, a derivative is a mathematical concept that measures the instantaneous rate of change of a function, while in finance, a derivative is a type of financial contract whose value is dependent on an underlying asset, group of assets, or benchmark.
