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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 AliasIndicatorpdAliasIndicator 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 AliasIndicator,AliasIndicator, 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.