Question:
Choose the correct alternative in the following:
If $y=\sqrt{\sin x+y}$, then $\frac{d y}{d x}$ equals.
A. $\frac{\cos x}{2 y-1}$
B. $\frac{\cos x}{1-2 y}$
c. $\frac{\sin x}{1-2 y}$
D. $\frac{\sin x}{2 y-1}$
Solution:
$y=\sqrt{\sin x+y}$
Squaring both sides, we get
$y^{2}=\sin x+y$
Differentiating w.r.t y we get
$2 y=\cos x \frac{d x}{d y}+1$
$\frac{\mathrm{dx}}{\mathrm{dy}}=\frac{2 \mathrm{y}-1}{\cos \mathrm{x}}$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\cos \mathrm{x}}{2 \mathrm{y}-1}$
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