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In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its 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 derivatives market is the financial market for derivatives - financial instruments like futures contracts or options - which are derived from other forms of assets. The market can be divided into two, that for exchange-traded derivatives and that for over-the-counter derivatives. The legal nature of these products is very different, as well ...
Derivative (set theory), a concept applicable to normal functions; Derivative (graph theory), an alternative term for a line graph deva; Derivative (finance), a contract whose value is derived from that of other quantities; Derivative suit or derivative action, a type of lawsuit filed by shareholders of a corporation
In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements: an item (the "underlier") that can or must be bought or sold, a future act which must occur (such as a sale or purchase of the underlier),
Rigorously, a subderivative of a convex function : at a point in the open interval is a real number such that () for all .By the converse of the mean value theorem, the set of subderivatives at for a convex function is a nonempty closed interval [,], where and are the one-sided limits = (), = + ().
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.
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Derivation (differential algebra), a unary function satisfying the Leibniz product law Formal proof or derivation, a sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference