The "error" is a side effect of doing the derivative badly, sorry.
Nice try, though. I am glad you are exploring rather than just doing the assigned problems. Keep asking questions.
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?