d dx ( ^ - 1 1 + x 2 ) =

MCQ

${d \over {dx}}\left( {{{\cos }^{ - 1}}\sqrt {{{1 + \cos x} \over 2}} } \right) = $

A
$1$
✓
${1 \over 2}$
C
${1 \over 3}$
D
None of these

✓

Answer

Correct option: B.

${1 \over 2}$

b
(b) $\frac{d}{{dx}}\left( {{{\cos }^{ - 1}}\sqrt {\frac{{1 + \cos x}}{2}} } \right) = \frac{d}{{dx}}\left[ {{{\cos }^{ - 1}}\left( {\cos \frac{x}{2}} \right)} \right] = \frac{1}{2}$.

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