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D

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

D can be used to find the rate of change of a function.
D[f, x] can be input as  . The character  is entered as AliasIndicatorpdAliasIndicator 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].
FilledSquare f''[x] denotes the second derivative of f with respect to 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 AliasIndicator,AliasIndicator, 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.

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.

Here is the Chain Rule of first-year calculus.

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

This gives the fourth derivative of  with respect to x.

Here is the partial derivative  .

Mathematical Input Notation

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

This also gives the partial derivative  .



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