Can someone show me how to differentiate (1+x+x^2)(2-x^4)? Unsure of my work Thanks!?

Two ways.
(1) f(x) = g(x) h(x)
f'(x) = gh' + g'h
= (1 + x + x^2)(-4x^3) + (1+2x)(2 - x^4)
= -4x^3 - 4x^4 - 4x^5 + 2 + 4x - x^4 - 2x^5
= 2 + 4x - 4x^3 - 5x^4 - 6x^5

(2) f(x) = 2 + 2x + 2x^2 - x^4 - x^5 - x^6
f'(x) = 2 + 4x - 4x^3 -5x^4 - 6x^5

As you'd expect, it doesn't matter which way you do it.