You made a mistake applying the "derivative of a product" formula.
g'(x) = (3x^2)(3x^2-1) + (x^3+1)*6x
= 12x^4 -3x^2 +6x
= 3x(4x^3 -x^2 +2)
Actually I figure it out.
In google type: calc101
When you see list of resultc click on:
Calc101com Automatic Calculus and Algebra Help
When page be open clik option: derivatives
When this page be open in rectacangle type:
and click options DO IT
You will see solution step-by-step
By the way on this site you can practice any kind of derivation.
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