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.
