If `y=xsiny ,` prove that `(dy)/(dx)=(siny)/((1-xcosy))`

Explanation

`y=x \sin y`



Differentiating win.t. ' `x` ',
$$
\begin{aligned}
\frac{d y}{d x} &=\frac{d}{d x}(x \sin y) \\
&=\frac{d}{d x}(x) \cdot(\sin y)+x \frac{d}{d x}(\sin y) \\
\Rightarrow \frac{d y}{d x} &=\sin y+x \cos y \frac{d y}{d x} . \\
...