If $z= xy \text{ ln} (xy)$, then
- $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}= 0 \\$
- $y\frac{\partial z}{\partial x}= x\frac{\partial z}{\partial y} \\$
- $x\frac{\partial z}{\partial x}= y\frac{\partial z}{\partial y} \\$
- $y\frac{\partial z}{\partial x}+x\frac{\partial z}{\partial y}= 0$