Problem 1264 (difficulty: 8/10)

Prove that if \(\displaystyle D_{12}f\) and \(\displaystyle D_{21}f\) exist in a neighborhood of \(\displaystyle (a,b)\) and they are both continuous at \(\displaystyle (a,b)\) then \(\displaystyle D_{12}f(a,b)=D_{21}f(a,b)\).

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