If sin(x + y) = log(x + y), then dy/dx=

$\cos (x+y)\left(1+\frac{d y}{d x}\right)=\frac{1}{x+y}\left(1+\frac{d y}{d x}\right)$

$\Rightarrow \left[\cos (x+y)-\frac{1}{x+y}\right]\left(1+\frac{d y}{d x}\right)=0$

$\Rightarrow \frac{d y}{d x}=-1$

Hence (4) is correct answer.