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D

  • D[ f , x ] gives the partial derivative .
  • D[ f , { x , n }] gives the multiple derivative .
  • D[ f , , , ... ] gives .
  • can be used to find the rate of change of a function.
  • D[ f , x ] can be input as . The character is entered as pd or \ [PartialD] . The variable x is entered as a subscript.
  • An alternative notation for taking the derivative of a function of one variable is f ' [ x ] which is equivalent to D[ f [ x ] , x ] .
    f '' [ x ] denotes the second derivative of f x
  • All quantities that do not explicitly depend on the are taken to have zero partial derivative.
  • The derivatives of built-in mathematical functions are evaluated when possible in terms of other built-in mathematical functions.
  • 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 also: Integrate , ND .


    Examples

    Using InstantCalculators

    Here are the InstantCalculators for the D function. Enter the parameters for your calculation and click Calculate to see the result.

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    Entering Commands Directly

    You can paste a template for this command via the Text Input button on the D Function Controller.

    Here is the derivative of with respect to x .

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    Here is the Chain Rule of first-year calculus.

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    If you differentiate a function with respect to x , say, all other parameters are treated as constants.

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    This gives the fourth derivative of with respect to x .

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    Here is the partial derivative .

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    Mathematical Input Notation

    This also gives the fourth derivative of with respect to x .

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    This also gives the partial derivative .

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