Answer
$f_{xyy}=f_{yxy}=f_{yyx}$
Work Step by Step
Consider, we have $f_{xyy}=(f_{xy})_{y}$ ...(1)
$f_{yxy}=(f_{yx})_{y}$ ...(2)
From the equations (1) and (2), we get
$(f_{xy})_{y}=(f_{xy})_{y}=f_{xyy}$
This yields: $f_{yxy}=f_{xyy}$
Since, $ f_{yyx}=(f_{y})_{yx}\\(f_{y})_{yx}$=$(f_{y})_{xy}$
Thus, we have
$f_{yyx}=(f_{y})_{xy}=f_{yxy}$
$\implies f_{yxy}=f_{yxy},$
Transitive property of equality defines as: $f_{xyy}=f_{yxy}=f_{yyx}$
