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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $u = {\sin ^{ - 1}}\left( {{y \over x}} \right),$ then ${{\partial u} \over {\partial x}}$ is equal to
  • A
    $ - {y \over {{x^2} + {y^2}}}$
  • B
    ${x \over {\sqrt {1 - {y^2}} }}$
  • C
    ${{ - y} \over {\sqrt {{x^2} - {y^2}} }}$
  • ✓
    ${{ - y} \over {x\sqrt {{x^2} - {y^2}} }}$
✓

Answer

Correct option: D.
${{ - y} \over {x\sqrt {{x^2} - {y^2}} }}$
d
(d) $u = {\sin ^{ - 1}}\frac{y}{x}$;

$\therefore $ $\frac{{\partial u}}{{\partial x}} = \frac{1}{{\sqrt {1 - \frac{{{y^2}}}{{{x^2}}}} }}.\left( { - \frac{y}{{{x^2}}}} \right) = - \frac{y}{{x\sqrt {{x^2} - {y^2}} }}$.

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