Question

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

Answer 1

Given : $y+\sin y=\cos x$ .............. $\left(1\right)$

Now differentiate the given expression $\left(1\right)$ with respective to $x$, we get

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

$⟹\frac{dy}{dx}(1+\cos y)=-\sin x$

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