Question

Solve using implicit derivative
cuberoot(x)+cuberoot(xy)=4y^2

Answer 1

x^(1/3) + (xy)^(1/3) = 4y^2
1/3 x^(-2/3) + 1/3 (xy)^(-2/3) (y + xy') = 8yy'

Now just solve that for y'. There are several ways to massage the final answer.