y'(x)=\frac{4 (a-1) (a+1) x \left(a^2 x^2-x^2-y(x)^2-2\right)}{a^8 x^6-4 a^6 x^6-3 a^6 x^4 y(x)^2+6 a^4 x^6+9 a^4 x^4 y(x)^2+3 a^4 x^2 y(x)^4-4 a^2 x^6-9 a^2 x^4 y(x)^2-6 a^2 x^2 y(x)^4+4 a^2 x^2 y(x)-a^2 y(x)^6+x^6+3 x^4 y(x)^2+3 x^2 y(x)^4-4 x^2 y(x)+y(x)^6-4 y(x)^3-8 y(x)}