Question

How do you find the derivative of `x^3(4x^2-1)^3`?

Answer 1

I would use the Product and Chain Rule (to deal with the `()^3`):
`3x^2(4x^2-1)^3+x^3*3(4x^2-1)^2*8x=`
`=(4x^2-1)^2[3x^2(4x^2-1)+24x^4]=`
`=(4x^2-1)^2[36x^4-3x^2]=(4x^2-1)^2[12x^2-1]3x^2`