Dt

Dt[f,x]
gives the total derivative .

Dt[f]
gives the total differential .

Dt[f,{x,n}]
gives the multiple derivative .

Dt[f,x1,x2,]
gives .

Details and OptionsDetails and Options

  • Dt[f,x1,,Constants->{c1,}] specifies that the 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 .
  • You can specify total derivatives by assigning values to Dt[f], etc.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Find the total derivative with respect to :

In[1]:=
Click for copyable input
Out[1]=

Find the total derivative of :

In[1]:=
Click for copyable input
Out[1]=

Find the second total derivative with respect to :

In[1]:=
Click for copyable input
Out[1]=

Find the total derivative with respect to two variables:

In[1]:=
Click for copyable input
Out[1]=
Introduced in 1988
(1.0)