If $y= \frac{x}{x^2+\frac{x}{x^2+\frac{x}{x^2+....}}}$ and $\int\frac{y-x^2}{(x^2+y)(x+y^2)}dx = f(y)+c$, determine the value of $f'(y)$ for $x=1$
My approach: $y = \frac{x}{x^2+y} \Rightarrow \frac{y}{x}=x^2+y \Rightarrow \ln y = \ln x + \ln(x^2+y) \Rightarrow \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{x^2+y}(2x+\frac{dy}{dx}) $
Simplifying further creates a mess that is nowhere similar to the integral expression for $f(y)$. Can someone help me with what I am missing here?