Mixed Derivatives and Symmetry of The Hessian
The mixed derivatives of f are the entries off the main diagonal in the Hessian. Assuming that they are continuous, the order of differentiation does not matter (Clairaut's theorem). For example,
This can also be written as:
In a formal statement: if the second derivatives of f are all continuous in a neighborhood D, then the Hessian of f is a symmetric matrix throughout D; see symmetry of second derivatives.
Read more about this topic: Hessian Matrix
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