This is documentation for Mathematica 5.2, which was
based on an earlier version of the Wolfram Language.

# D

Usage

D[f, x] gives the partial derivative .
D[f, {x, n}] gives the multiple derivative .
D[f, x, y, ... ] gives .
D[f, {{, , ... }}] for a scalar gives the vector derivative .

Notes

D[f, x] can be input as . The character is entered as pd or \[PartialD]. The variable x 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, , ... , NonConstants -> {, ... }] specifies that every implicitly depends on every , 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 n times. If f is a scalar, a list has depth 1, then the result is a tensor of rank n, as in the term of the multivariate Taylor series of f.
D[f, {}, {}, ... ] is normally equivalent to First[Outer[D, {f}, , , ... ]].
• 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 ,, can be used instead of an ordinary comma. It does not display, but is still interpreted just like a comma.
• Implementation notes: see Section A.9.5.
• New in Version 1; modified in 5.1.