] gives the partial derivative .
] gives the multiple derivative .
, ... ] gives .
] 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.
, ... ,
] 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.
] 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, Section 3.5.1.
See also: Dt, Derivative.
Related package: Calculus`VectorAnalysis`, NumericalMath`NLimit`.
Here is the derivative of with respect to x.
Here is the familiar Chain Rule of first year calculus.
This gives the fourth derivative of .
Here is the partial derivative .
Normally, if you differentiate a function with respect to x, say, Mathematica will treat all other parameters as constants.
By specifying that t depends upon x, you can get the desired result for such expressions.
Here are some advanced examples.
Sometimes the derivative is kept unevaluated until an argument is substituted for which an evaluation can be given.
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