Problem 1265 (difficulty: 8/10)

Prove that if \(\displaystyle D_{1}f\), \(\displaystyle D_2f\) and \(\displaystyle D_{12}f\) exist in a neighborhood of \(\displaystyle (a,b)\) and \(\displaystyle D_{12}\) is continuous at \(\displaystyle (a,b)\), then \(\displaystyle D_{21}\) exists and \(\displaystyle D_{12}f(a,b)=D_{21}f(a,b)\). (Schwarz)

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