This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Dt

 Dtgives the total derivative . Dt[f]gives the total differential . Dtgives the multiple derivative . Dtgives .
• 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.
Find the total derivative with respect to :
Find the total derivative of :
Find the second total derivative with respect to :
Find the total derivative with respect to two variables:
Find the total derivative with respect to :
 Out[1]=

Find the total derivative of :
 Out[1]=

Find the second total derivative with respect to :
 Out[1]=

Find the total derivative with respect to two variables:
 Out[1]=
 Scope   (4)
The total derivative of a constant is 0:
Total derivative of a general monomial:
Total derivative of a trigonometric function:
Rules for total differentiation including sums:
Products:
Quotients:
Composition:
Logarithmic total derivative:
 Options   (3)
Specify that is constant with respect to :
Specify that and are constant with respect to :
Use TagSet to specify a constant:
The total derivative of a function of alone is the same as its derivative:
New in 1