Problem 1276 (difficulty: 7/10)

Prove that if \(\displaystyle f:\R^2\to\R\) is differentiable and \(\displaystyle D_1f(x,y) = yD_2f(x,y)\) for all \(\displaystyle x,y\), then there is a \(\displaystyle g:\R\to\R\) differentiable function for which \(\displaystyle f(x,y)=g(e^xy)\).

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