Question

If $y=\sqrt{\sin x+y}$, then $\frac{dy}{dx}$ is

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

Answer 1

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

We have,

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

On squaring both the sides, we get

$y^2=\sin \left(x\right)+y$

Differentiating w.r.t. $x$,

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