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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
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
    ${2 \over {{{(x - y)}^2}}}$
✓

Answer

Correct option: B.
${2 \over {x - y}}$
b
(b) $u = \frac{{x + y}}{{x - y}}$

$\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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