> > > reduce the risk of error.
< < <
f(x)=x2(5x2−2)4=uv where u=x2, v=w4, and w=(5x2−2)⟹f’=uv’+u’v, u’=2x, v’=4w3w’, and w‘=2∗5x=10x.∴f’=x2∗4w3w’+2xv=x2∗4w3∗10x+2xw4=2xw3(4∗5∗x2+w)=2xw3(20x2+5x2−2)=2x(x2−2)3(25x2−2)
Notice how much simpler that is than the gyrations of the OP.
Really!?