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Dt

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