If z = xy In(xy), then

1
\(x\frac{{\partial z}}{{\partial x}} + y\frac{{\partial z}}{{\partial y}} = 0\)
2
\(y\frac{{\partial z}}{{\partial x}} = x\frac{{\partial z}}{{\partial y}}\)
3
\(x\frac{{\partial z}}{{\partial x}} = y\frac{{\partial z}}{{\partial y}}\)
4
\(y\frac{{\partial z}}{{\partial x}} + x\frac{{\partial z}}{{\partial y}} = 0\)

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