This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# D ()

 D[f, x]gives the partial derivative . D[f, {x, n}]gives the multiple derivative . D[f, x, y, ...]differentiates successively with respect to . D[f, {{x1, x2, ...}}]for a scalar gives the vector derivative .
• D[f, x] can be input as . The character is entered as Esc pd Esc or \[PartialD]. The variable is entered as a subscript.
• All quantities that do not explicitly depend on the variables given are taken to have zero partial derivative.
• D[f, var1, ..., NonConstants->{u1, ...}] specifies that every implicitly depends on every varj, so that they do not have zero partial derivative.
• D[f, {list}] threads D over each element of list.
• D[f, {list, n}] is equivalent to D[f, {list}, {list}, ...] where {list} is repeated times. If is a scalar, a list has depth 1, then the result is a tensor of rank , as in the term of the multivariate Taylor series of .
• D[f, {list1}, {list2}, ...] is normally equivalent to First[Outer[D, {f}, list1, list2, ...]].
• Numerical approximations to derivatives can be found using N.
• D uses the chain rule to simplify derivatives of unknown functions.
• D[f, x, y] can be input as . The character \[InvisibleComma], entered as Esc , Esc, can be used instead of an ordinary comma. It does not display, but is still interpreted just like a comma.
Derivative with respect to x:
 Out[1]=

4 derivative with respect to x:
 Out[1]=

Derivative with respect to x and y:
 Out[1]=

Derivative involving a symbolic function f:
 Out[1]=