A) \[\frac{1}{2}\sin z\]
B) \[\frac{1}{2}\tan z\]
C) \[0\]
D) None of these
Correct Answer: B
Solution :
\[\sin z\] is homogeneous in x, y of degree 1/2. \[\therefore \] \[x\frac{\partial }{\partial x}(\sin z)+y\frac{\partial }{\partial y}(\sin z)=\frac{1}{2}\sin z\] Þ\[\frac{dv}{dt}\] Þ \[x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}=\frac{1}{2}\tan z\].
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