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Dt
Dt
[
f
,
x
]
gives the total derivative
d
f
/
d
x
.
Dt
[
f
]
gives the total differential
df
.
Dt
[
f
, {
x
,
n
}]
gives the multiple derivative
d
n
f
/
d
x
n
.
Dt
[
f
,
x
1
,
x
2
,
...
]
gives
d
/
d
x
1
d
/
d
x
2
... f
.
MORE INFORMATION
Dt
[
f
,
x
1
,
...
,
Constants
->{
c
1
,
...
}]
specifies that the
c
i
are constants, which have zero total derivative.
Symbols with attribute
Constant
are taken to be constants, with zero total derivative.
If an object is specified to be a constant, then all functions with that object as a head are also taken to be constants.
All quantities not explicitly specified as constants are assumed to depend on the
x
i
.
You can specify total derivatives by assigning values to
Dt
[
f
]
, etc.
EXAMPLES
CLOSE ALL
Basic Examples
(2)
Find the total derivative with respect to
:
In[1]:=
Out[1]=
Find the total derivative of
:
In[1]:=
Out[1]=
SEE ALSO
D
Derivative
Constants
NonConstants
TUTORIALS
Differentiation
Total Derivatives
MORE ABOUT
Calculus
New in 1
© 2008 Wolfram Research, Inc.
EXAMPLES
Basic Examples 
