Mathematica 9 is now available
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Mathematica > Mathematics and Algorithms > Calculus >
Built-in Mathematica SymbolTutorials »|See Also »|More About »

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.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Find the total derivative with respect to x:
Find the total derivative of x y:
Find the second total derivative with respect to x:
Find the total derivative with respect to two variables:
Find the total derivative with respect to x:
In[1]:=
Click for copyable input
Out[1]=
 
Find the total derivative of x y:
In[1]:=
Click for copyable input
Out[1]=
 
Find the second total derivative with respect to x:
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]=
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 a is constant with respect to x:
Specify that a and b are constant with respect to x:
Use TagSet to specify a constant:
Properties & Relations   (1)
The total derivative of a function of x alone is the same as its derivative:
New in 1
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team