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D

FilledSmallSquare D[f, x] gives the partial derivative .

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

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

FilledSmallSquare D can be used to find the rate of change of a function.

FilledSmallSquare D[f, x] can be input as . The character is entered as AliasIndicatorpdAliasIndicator or \[PartialD]. The variable x is entered as a subscript.

FilledSmallSquare An alternative notation for taking the derivative of a function of one variable is f'[x] which is equivalent to D[f[x], x].

FilledSquaref''[x] denotes the second derivative of f with respect to x.

FilledSmallSquare All quantities that do not explicitly depend on the are taken to have zero partial derivative.

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

FilledSmallSquare D uses the chain rule to simplify derivatives of unknown functions.

FilledSmallSquare D[f, x, y] can be input as . The character \[InvisibleComma], entered as AliasIndicator,AliasIndicator, can be used instead of an ordinary comma. It does not display but is still interpreted just like a comma.

FilledSmallSquare 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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