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Dt

  • Dt[ f , x ] gives the total derivative .
  • Dt[ f ] gives the total differential .
  • Dt[ f , x , n ] gives the multiple derivative .
  • Dt[ f , , , ... ] gives .
  • Dt[ f , , ... , Constants -> , ... ] 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 .
  • Example: Dt[x y].
  • Dt[x y, Constants -> x ].
  • You can specify total derivatives by assigning values to Dt[ f ], etc.
  • See the Mathematica book: Section 1.5.2Section 3.5.2.
  • See also: D, Derivative.

    Further Examples

    This gives the total derivative of with respect to x.

    In[1]:=

    Out[1]=

    This gives the total differential.

    In[2]:=

    Out[2]=

    This gives the second derivative with respect to x.

    In[3]:=

    Out[3]=

    This gives a multiple derivative.

    In[4]:=

    Out[4]=