Continuity and Differentiability — Maths STD 12 Science — Question

$\begin{array}{lr}\text { Taking } & y=x+\frac{1}{y} \\ \Rightarrow & y^2=x y+1 \\ \Rightarrow & y^2-x y=1\end{array}$
now differentiating w.r.t. $x$
$\Rightarrow \quad \frac{d}{d x}\left(y^2\right)-\frac{d}{d x}(x y)=\frac{d}{d x}(1)$
$\Rightarrow 2 y \frac{d y}{d x}-\left[x \cdot \frac{d y}{d x}+y \cdot 1\right]=0$
$\Rightarrow \quad 2 y \frac{d y}{d x}-\frac{x d y}{d x}-y=0$
$\Rightarrow \quad \frac{d y}{d x}(2 y-x)=y$
$\Rightarrow \quad \frac{d y}{d x}=\frac{y}{2 y-x}$