If y = x + y , then dy dx equals to - Vidyadip

MCQ

If $y = \sqrt {\sin x + y} ,$ then ${{dy} \over {dx}}$ equals to

A
${{\sin x} \over {2y - 1}}$
✓
${{\cos x} \over {2y - 1}}$
C
${{\sin x} \over {2y + 1}}$
D
${{\cos x} \over {2y + 1}}$

✓

Answer

Correct option: B.

${{\cos x} \over {2y - 1}}$

b
(b) $y = \sqrt {\sin x + y} ,$ ==> ${y^2} = \sin x + y$

Differentiate with respect to $ x$ ,

$2y.\frac{{dy}}{{dx}} = \cos x + \frac{{dy}}{{dx}}$

==> $\frac{{dy}}{{dx}}(2y - 1) = \cos x$

==> $\frac{{dy}}{{dx}} = \frac{{\cos x}}{{2y - 1}}$.

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