is the general form, representing a function obtained from
f
by differentiating
n
1
times with respect to the first argument,
n
2
times with respect to the second argument, and so on.
Derivative
is generated when you apply
D
to functions whose derivatives the Wolfram Language does not know.
The Wolfram Language attempts to convert
Derivative
[
n
]
[
f
]
and so on to pure functions. Whenever
Derivative
[
n
]
[
f
]
is generated, the Wolfram Language rewrites it as
D
[
f
[
#
]
,
{
#
,
n
}
]
&
. If the Wolfram Language finds an explicit value for this derivative, it returns this value. Otherwise, it returns the original
Derivative
form.
Derivative
[
-
n
]
[
f
]
represents the
n
indefinite integral of
f
.
Derivative
[
{
n
1
,
n
2
,
…
}
]
[
f
]
represents the derivative of
f
[
{
x
1
,
x
2
,
…
}
]
taken
n
i
times with respect to
x
i
. In general, arguments given in lists in
f
can be handled by using a corresponding list structure in
Derivative
.
N
[
f
'
[
x
]
]
will give a numerical approximation to a derivative.
indefinite integral of
