Question

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

Answer 1

Given $xsiny+ysinx=0$

Now differentiate the equation with respective to $x$

We get $siny+xcosy\frac{dy}{dx}+\frac{dy}{dx}sinx+ycosx=0$

$\Rightarrow \frac{dy}{dx}(xcosy+sinx)+(siny+ycosx)=0$

$\Rightarrow \frac{dy}{dx}=-\left(\frac{siny+ycosx}{xcosy+sinx}\right)$