Partial differential
of the first order of a function in several variables
The differential of the function with respect to one of the variables, keeping the remaining variables fixed. For example, if a function is defined in some neighbourhood of a point
, then the partial differential
of
with respect to the variable
at the given point is equal to the ordinary differential
at
of the function
in the single variable
, i.e.
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It follows that
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Partial differentials of order are defined analogously. For example, the partial differential
of order
of
with respect to
at
is just the
-th order differential of the function
in the single variable
at the point
. Hence,
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Comments
For references see Differential calculus and Differential.
Partial differential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Partial_differential&oldid=48133