derivativedɪˈrɪv ə tɪv
derivative (n)
- plural
- derivatives
English Definitions:
derived function, derivative, differential coefficient, differential, first derivative (noun)
the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx
derivative (noun)
a compound obtained from, or regarded as derived from, another compound
derivative instrument, derivative (noun)
a financial instrument whose value is based on another security
derivative (adj)
(linguistics) a word that is derived from another word
"`electricity' is a derivative of `electric'"
derivative (adj)
resulting from or employing derivation
"a derivative process"; "a highly derivative prose style"
derivative (Noun)
Something derived.
derivative (Noun)
A word that derives from another one.
derivative (Noun)
A financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.
derivative (Noun)
A chemical derived from another.
derivative (Noun)
The derived function of a function.
derivative (Noun)
The value of this function for a given value of its independent variable.
derivative (Adjective)
Imitative of the work of someone else.
derivative (Adjective)
Referring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.
derivative (Adjective)
Having a value that depends on an underlying asset of variable value.
derivative (Adjective)
Lacking originality.
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. Informally, the derivative is the ratio of the infinitesimal change of the output over the infinitesimal change of the input producing that change of output. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely related notion is the differential of a function. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.
Derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. 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. Derivatives can be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus relates antidifferentiation with integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.
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"derivative." Kamus.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.kamus.net/english/derivative>.
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