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 The Mathematica Book: Section 1.5.2 and Section 3.5.1.
Implementation Notes: see section A.9.5.
See also: Dt, Derivative.
Related packages: Calculus`VectorAnalysis`, NumericalMath`NLimit`.