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Dt

Dt[f, x]
gives the total derivative df/dx.
Dt[f]
gives the total differential df.
Dt[f, {x, n}]
gives the multiple derivative dnf/dxn.
Dt[f, x1, x2, ...]
gives d/dx1 d/dx2 ... f.
  • Dt[f, x1, ..., Constants->{c1, ...}] specifies that the ci 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 xi.
  • You can specify total derivatives by assigning values to Dt[f], etc.
Find the total derivative with respect to x:
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Click for copyable input
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Find the total derivative of x y:
In[1]:=
Click for copyable input
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