If sin(x + y) = log(x + y), then $\frac{dy}{dx}=$

2 -2 1 -1

-1

$\cos (x+y)\left(1+\frac{d y}{d x}\right)=\frac{1}{x+y}\left(1+\frac{d y}{d x}\right)$ $\Rightarrow \left[\cos (x+y)-\frac{1}{x+y}\right]\left(1+\frac{d y}{d x}\right)=0$ $\Rightarrow \frac{d y}{d x}=-1$ Hence (4) is correct answer.