[RESOLVED] Implicit Differentiation

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This is a problem out of Shaum's Outlines on Numerical Methods. Just some spare time fun.
Differentiate the following function wrt x (i.e. find y'):

x³y⁴ + 2y = 3x

The solution from the back of the book is y' = y(1-x²y⁴) / x(1+x²y⁴))

I know the solution is right because I checked it using RK4. I didn't think my differentiation skills were THAT rusty, but I come up with something different.

Differentiating both sides I get:

(1) 3x²y⁴ + 4x³y³y' + 2y' = 3

(2) y' (4x³y³ + 2) = (3 - 3x²y⁴)

(3) y' = (3 - 3x²y⁴) / (4x³y³ + 2)

Can anyone point out my error(s)? Thanks.