Differentiate given
$\frac{y}{x-y}=x^2+1$
Initially I wanted to use the quotient rule to solve this, but then I tried differentiating it as it is:
$\frac {y_\frac{dy}{dx}}{1-y_\frac{dy}{dx}}=2x$
$\frac{dy}{dx}(y y^{-1})=2x$
$\frac{dy}{dx}=\frac{2x}{yy^{-1}}$
$\frac{dy}{dx}=\frac{2xy}{y}$
$\frac{dy}{dx}=2x$
I am wondering how I can check to see if this is a valid answer?