Question

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

• A. $\frac{\cos x}{2y-1}$
• B. $\frac{\cos }{1-2y}$
• C. $\frac{\sin x}{1-2y}$
• D. $\frac{\sin x}{2y-1}$

Answer 1

The correct option is A $\frac{\cos x}{2y-1}$

Given, $y=\sqrt{\sin x+y}$

$⟹y^2=\sin x+y$

Differentiate w.r.t. $x$,

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

$⟹\frac{dy}{dx}=\frac{\cos x}{2y-1}$