Solve for f_y
f_{y}=yz\ln(xy)
\left(x<0\text{ and }y<0\right)\text{ or }\left(x>0\text{ and }y>0\right)
Solve for x
\left\{\begin{matrix}x=\frac{e^{\frac{f_{y}}{yz}}}{y}\text{, }&yz\neq 0\\x>0\text{, }&y>0\text{ and }f_{y}=0\text{ and }z=0\\x<0\text{, }&y<0\text{ and }f_{y}=0\text{ and }z=0\end{matrix}\right.
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