A) \[y\frac{\partial z}{\partial y}\]
B) \[-y\frac{\partial z}{\partial y}\]
C) \[2y\frac{\partial z}{\partial y}\]
D) \[2y\frac{\partial z}{\partial x}\]
Correct Answer: B
Solution :
Since z is homogeneous in x, y of order ?0?. \[\therefore \] By Euler?s theorem \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=\] 0 Þ \[x\frac{\partial z}{\partial x}=-y\frac{\partial z}{\partial y}\]
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