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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 the Mathematica book: Section 1.5.2Section 3.5.1.
  • See also: Dt, Derivative.
  • Related package: Calculus`VectorAnalysis`, NumericalMath`NLimit`.

    Further Examples

    Here is the derivative of with respect to x.

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    Here is the familiar Chain Rule of first year calculus.

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    This gives the fourth derivative of .

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    Here is the partial derivative .

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    Normally, if you differentiate a function with respect to x, say, Mathematica will treat all other parameters as constants.

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    By specifying that t depends upon x, you can get the desired result for such expressions.

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    Here are some advanced examples.

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    Sometimes the derivative is kept unevaluated until an argument is substituted for which an evaluation can be given.

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