# Mixed partial derivative given first and second order derivative

by matt   Last Updated May 16, 2019 04:20 AM

If $$f_x=f_y=f_{xx}=f_{yy}=1$$ at a point, does it imply $$f_{xy}=f_{yx}=1$$ at that point.

Note this is not a homework problem, it is a question from a book I am reading for which the solution just regards $$f_{xy}=f_{yx}=1$$ given $$f_x=f_y=f_{xx}=f_{yy}=1$$ (Thomas Calculus 12th edition page 832 question 96). So I was wondering if there was a mistake in the question which is, simply forgetting to add $$f_{xy}=f_{yx}=1$$ as a premise.

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