SOLUTIONS

BUILTIN MATHEMATICA SYMBOL
D
D[f, x]
gives the partial derivative .
D[f, {x, n}]
gives the multiple derivative .
D[f, x, y, ...]
differentiates f successively with respect to .
D[f, {{x_{1}, x_{2}, ...}}]
for a scalar f gives the vector derivative .
D[f, {array}]
gives a tensor derivative.
Details and OptionsDetails and Options
 D[f, x] can be input as . The character is entered as EscpdEsc or . 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, var_{1}, ..., NonConstants>{u_{1}, ...}] specifies that every implicitly depends on every , so that they do not have zero partial derivative.
 D[f, ...] threads over lists that appear in f.
 D[f, {list}] effectively 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, and list has depth 1, then the result is a tensor of rank n, as in the n term of the multivariate Taylor series of f.
 D[f, {list_{1}}, {list_{2}}, ...] is normally equivalent to First[Outer[D, {f}, list_{1}, list_{2}, ...]].
 If f is a list, then D[f, {list}] effectively threads first over each element of f, and then over each element of list. The result is an array with dimensions Join[Dimensions[f], Dimensions[list]].
 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 , entered as Esc,Esc, can be used instead of an ordinary comma. It does not display, but is still interpreted just like a comma.
 If any of the arguments to D are SparseArray objects, the result will be a SparseArray object. »
ExamplesExamplesopen allclose all
Basic Examples (7)Basic Examples (7)
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Fourth derivative with respect to :
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Derivative with respect to and :
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Derivative involving a symbolic function :
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Vector derivative (gradient vector):
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Secondorder derivative tensor:
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Evaluate derivatives numerically:
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Enter using EscpdEsc, and subscripts using Control+_:
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