If y = ( x + x ), then dy dx = - Vidyadip

MCQ

If $y = \sin (\sqrt {\sin x + \cos x} )$, then ${{dy} \over {dx}} = $

A
${1 \over 2}{{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}$
B
${{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}$
✓
${1 \over 2}{{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}.(\cos x - \sin x)$
D
None of these

✓

Answer

Correct option: C.

${1 \over 2}{{\cos \sqrt {\sin x + \cos x} } \over {\sqrt {\sin x + \cos x} }}.(\cos x - \sin x)$

c
(c) $y = \sin (\sqrt {\sin x + \cos x} )$

$\frac{{dy}}{{dx}} = \frac{1}{2}\frac{{\cos (\sqrt {\sin x + \cos x} )}}{{\sqrt {\sin x + \cos x} }}(\cos x - \sin x)$.

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