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''of a function in  $  n $
variables at a point  $  x _ {0} \in \mathbf R  ^ {n} $''

The same as the [[Differential|differential]] of the function at that point. The term complete differential is used to contrast it with the term partial differential. The concept of the complete differential of a function in  $  n $
variables can be extended to the case of mappings of open sets in linear topological spaces into similar spaces (see [[Gâteaux differential|Gâteaux differential]]; [[Fréchet differential|Fréchet differential]]; [[Differentiation of a mapping|Differentiation of a mapping]]).