MCQ
If $u = {{x + y} \over {x - y}}$, then ${{\partial u} \over {\partial x}} + {{\partial u} \over {\partial y}} = $
- A${1 \over {x - y}}$
- ✓${2 \over {x - y}}$
- C${1 \over {{{(x - y)}^2}}}$
- D${2 \over {{{(x - y)}^2}}}$
$\therefore \frac{{\partial u}}{{\partial x}} = \frac{{(x - y)\,.\,1 - (x + y)\,.\,1}}{{{{(x - y)}^2}}}$$ = \frac{{ - 2y}}{{{{(x - y)}^2}}}$
$\frac{{\partial u}}{{\partial y}} = \frac{{(x - y).1 - (x + y)( - 1)}}{{{{(x - y)}^2}}} $
$ = \frac{{2x}}{{{{(x - y)}^2}}}$
$\therefore $ $\frac{{\partial u}}{{\partial x}} + \frac{{\partial u}}{{\partial y}} = \frac{{2(x - y)}}{{{{(x - y)}^2}}} = \frac{2}{{x - y}}$.
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