Why do I get different answers when doing this?

Take, for example, this equation:

y = (x^3)/3 + 1/4x; the derivative would then be y' = x^2 + 1/4.

But, if we were to re-write the equation by taking out an x, finding the derivative using the product rule gives you different answer.

y = (x^3)/3 + 1/4x

y = x((x^2)/3 + 1/4)

y' = 1((x^2)/3 + 1/4) + x(x/6)

y' = (x^2)/3 + 1/4 + (x^2)/6

y' = (x^2)/2 + 1/4

How is this possible?