MCQ
જો $u = {\tan ^{ - 1}}{y \over x}$, તો $x{{\partial u} \over {\partial x}} + y{{\partial u} \over {\partial y}} = $
- A$\tan u$
- B$\sin u$
- ✓$0$
- D$\cos 2u$
Clearly $u$ is homogeneous in $ x, y$ of degree $ 0.$
$\therefore $ By Euler’s theorem $x\frac{{\partial u}}{{\partial x}} + y\frac{{\partial u}}{{\partial z}} = 0\cdot u = 0$.
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