D

D[f, x] gives the partial derivative .

D[f, x, n] gives the multiple derivative .

D[f, , , ... ] gives .

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 are taken to have zero partial derivative.

D[f, , ... , NonConstants -> , ... ] specifies that the implicitly depend on the , so that they do not have zero partial derivative.

The derivatives of built-in mathematical functions are evaluated when possible in terms of other built-in mathematical functions.

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.

See Section 1.5.2 and Section 3.5.1.

Implementation Notes: see Section A.9.5.

See also: Dt, Derivative, Maximize.

Related packages: Calculus`VectorAnalysis`, NumericalMath`NLimit`.

New in Version 1; modified in 3.

Further Examples