Answer
$f_{xyy}=f_{yxy}=f_{yyx}$
Work Step by Step
Here, we have $f_{xyy}=(f_{xy})_{y}$
and $ f_{yxy}=(f_{yx})_{y}$
Further, $(f_{xy})_{y}=(f_{xy})_{y}=f_{xyy}$
This implies that $f_{yxy}=f_{xyy}$
Since, $ f_{yyx}=(f_{y})_{yx}$ and $(f_{y})_{yx}$=$(f_{y})_{xy}$
we have
$f_{yyx}=(f_{y})_{xy}=f_{yxy}$
This gives: $f_{yxy}=f_{yxy},$
As per the transitive property of equality, we get
$f_{xyy}=f_{yxy}=f_{yyx}$
