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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = \sin (2{\sin ^{ - 1}}x),$ then ${{dy} \over {dx}} = $
  • ✓
    ${{2 - 4{x^2}} \over {\sqrt {1 - {x^2}} }}$
  • B
    ${{2 + 4{x^2}} \over {\sqrt {1 - {x^2}} }}$
  • C
    ${{2 - 4{x^2}} \over {\sqrt {1 + {x^2}} }}$
  • D
    ${{2 + 4{x^2}} \over {\sqrt {1 + {x^2}} }}$
✓

Answer

Correct option: A.
${{2 - 4{x^2}} \over {\sqrt {1 - {x^2}} }}$
a
(a) Let $x = \sin \theta \Rightarrow 2{\sin ^{ - 1}}x = 2\theta $

==> $y = \sin 2\theta $

==>$\frac{{dy}}{{dx}} = \frac{{dy/d\theta }}{{dx/d\theta }} = \frac{{2\cos 2\theta }}{{\cos \theta }}$

$ = \frac{{2(1 - 2{{\sin }^2}\theta )}}{{\sqrt {1 - {{\sin }^2}\theta } }} = \frac{{2 - 4{x^2}}}{{\sqrt {1 - {x^2}} }}$.

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