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Is it possible to write the following equation in an even simpler form? (In other words does this have any specific implications on the form $\vec f(\vec x)$ can take?) $${\partial f_j(\vec x)\over \partial x_i}={\partial f_i(\vec x)\over \partial x_j}$$ where $x_k$ are components of $\vec x$ and $f_k(\vec x)$ are the components of $\vec f(\vec x)$.

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