Your roots are good: 5th roots of unity - Wolfram|Alpha
Simplifying the implicit differentiation is a bit messy but I'm pretty sure I don't like your (x^2)'s in the denominator.
Just in case a picture helps...
... where (key in spoiler) ...
I hope that helps.
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!