Implicit Derivative

Question

I did lots of calculation, but it just only going to be nothing but mess. If anyone could help me, thanks.

Answer 1

HINT: Let $a=s^2t,b=st^2$. Then you have the two equations $$x^2-2y^2a-2b=1\\ x^2+2y^2a+5b=1$$ Solve for $a,b$ and then eliminate $s$ by finding $st=(ab)^{1/3}$. Then do partial differentiation of $t$ with respect to $y$ twice.