Définitions
1.AdjectiveObtained by derivation; not radical, original, or fundamental."a derivative conveyance; a derivative word"
2.AdjectiveImitative of the work of someone else.
3.AdjectiveReferring to a work, such as a translation or adaptation, based on another work that may be subject to copyright restrictions.
4.AdjectiveHaving a value that depends on an underlying asset of variable value.
5.NounSomething derived.
6.NounA word formed by derivation, such as stylish from style.
7.NounA financial instrument whose value depends on the valuation of an underlying asset; such as a warrant, an option etc.
8.NounA chemical derived from another.
9.NounOne of the two fundamental objects of study in calculus (the other being integration), which quantifies the rate of change, tangency, and other qualities arising from the local behavior of a function.
The derived function of
f
(
x
)
{\displaystyle f(x)}
: the function giving the instantaneous rate of change of
f
{\displaystyle f}
; equivalently, the function giving the slope of the line tangent to the graph of
f
{\displaystyle f}
. Written
f
′
(
x
)
{\displaystyle f'(x)}
or
d
f
d
x
{\displaystyle {\frac {df}{dx}}}
in Leibniz's notation,
f
˙
(
x
)
{\displaystyle {\dot {f}}(x)}
in Newton's notation (the latter used particularly when the independent variable is time)."The derivative of
x
2
{\displaystyle x^{2}}
is
2
x
{\displaystyle 2x}
; if
f
(
x
)
=
x
2
{\displaystyle f(x)=x^{2}}
, then
f
′
(
x
)
=
2
x
{\displaystyle f'(x)=2x}
; The derivative of
f
(
x
)
=
x
3
{\displaystyle f(x)=x^{3}}
at
x
=
2
{\displaystyle x=2}
is
12
{\displaystyle 12}
."
10.NounThe derived function of
f
(
x
)
{\displaystyle f(x)}
: the function giving the instantaneous rate of change of
f
{\displaystyle f}
; equivalently, the function giving the slope of the line tangent to the graph of
f
{\displaystyle f}
. Written
f
′
(
x
)
{\displaystyle f'(x)}
or
d
f
d
x
{\displaystyle {\frac {df}{dx}}}
in Leibniz's notation,
f
˙
(
x
)
{\displaystyle {\dot {f}}(x)}
in Newton's notation (the latter used particularly when the independent variable is time)."The derivative of
x
2
{\displaystyle x^{2}}
is
2
x
{\displaystyle 2x}
; if
f
(
x
)
=
x
2
{\displaystyle f(x)=x^{2}}
, then
f
′
(
x
)
=
2
x
{\displaystyle f'(x)=2x}
"
11.NounThe value of such a derived function for a given value of its independent variable: the rate of change of a function at a point in its domain."The derivative of
f
(
x
)
=
x
3
{\displaystyle f(x)=x^{3}}
at
x
=
2
{\displaystyle x=2}
is
12
{\displaystyle 12}
."
12.NounAny of several related generalizations of the derivative: the directional derivative, partial derivative, Fréchet derivative, functional derivative, etc.
13.NounThe linear operator that maps functions to their derived functions, usually written
D
{\displaystyle D}
; the simplest differential operator.