Question

How do you differentiate `x^(2/3)+y^(2/3)=4`?

Answer 1

In this case of implicit differentiation consider that `y` is function of `x` so you get:
`2/3x^(2/3-1)+2/3y^(2/3-1)dy/dx=0`
`dy/dx=-(x^(-1/3))/(y^(-1/3))=-root3(y/x)`

Where `y=(4-x^(2/3))^(3/2)` from your original expression.