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If $z= xy \text{ ln} (xy)$, 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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