Question

Find $\frac{dy}{dx}$, if $x\sin y+y\sin x=0$.

Answer 1

$x\sin y+y\sin x=0$

Differentiating above equation w.r.t. $x$, we have

$(1.\sin y+\cos y\frac{dy}{dx}.x)+(\frac{dy}{dx}\sin x+\cos x.y)=0$

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

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