Assume that $f_{xy}$ and $f_{yx}$ are continuous and that $f_{yxx}$ exists. Show that $f_{xyx}$ also exists and that $f_{yxx} = f_{xyx}$.
2. $f_{yxx}$ means $(f_{yx})_x$. Since $f_{xy}$ and $f_{yx}$ are continuous, $f_{yx}= f_{xy}$.