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) ...

Spoiler:

Larger

I hope that helps.

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!