(x^3 +3y^4)^5=2xy find the derivative?

Question:use Implicit differentiation

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Answers:
5(x^3 + 3y^4)^4(3x^2 + 12y^3y') = 2xy' + 2y
5(x^3 + 3y^4)^4(3x^2) + 5(x^3 + 3y^4)^4(12y^3y') = 2xy' + 2y
15x^2(x^3 + 3y^4)^4 + 60y^3y'(x^3 + 3y^4)^4 = 2xy' + 2y
60y^3y'(x^3 + 3y^4)^4 - 2xy' = 2y - 15x^2(x^3 + 3y^4)^4
y'(60y^3(x^3 + 3y^4)^4 - 2x) = 2y - 15x^2(x^3 + 3y^4)^4
y' = (2y - 15x^2(x^3 + 3y^4)^4)/(60y^3(x^3 + 3y^4)^4 - 2x)

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15x^14+180x^11y^4+810x^8y^8+16...
and a partridge and a pair tree!

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