This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 MATHEMATICA TUTORIAL

# Derivatives of Unknown Functions

Differentiating a known function gives an explicit result.
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Differentiating an unknown function gives a result in terms of .
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Mathematica applies the chain rule for differentiation, and leaves the result in terms of .
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Differentiating again gives a result in terms of , , and .
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When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated.
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This represents . Mathematica assumes that the order in which derivatives are taken with respect to different variables is irrelevant.
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You can find the value of the derivative when by replacing with .
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 first derivative of a function of one variable n derivative of a function of one variable derivative of a function of several variables, times with respect to variable i

Output forms for derivatives of unknown functions.