Question

If $y+\sin y=\cos x$, find $\frac{dy}{dx}$

Answer 1

Given,

$y+\sin y=\cos x$

differentiating on both sides with respect to $x$

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

$\frac{dy}{dx}=-\frac{\sin x}{1+\cos y}$