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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
Differential coefficient of ${\sin ^{ - 1}}{{1 - x} \over {1 + x}} \,\,,w.r.t$ $\sqrt x $ is
  • A
    ${1 \over {2\sqrt x }}$
  • B
    ${{\sqrt x } \over {\sqrt {1 - x} }}$
  • C
    $1$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d) Let $y = {\sin ^{ - 1}}\frac{{1 - x}}{{1 + x}}$

==>$\frac{{dy}}{{dx}} = \frac{{ - 1}}{{\sqrt x (1 + x)}}$ ....$(i)$

and $z = \sqrt x $==>$\frac{{dz}}{{dx}} = \frac{1}{{2\sqrt x }}$ .....$(ii)$

Therefore by $(i)$ and $(ii)$

$\frac{{dy}}{{dz}} = \frac{{dy/dx}}{{dz/dx}} = \frac{{ - 2}}{{1 + x}}$.

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