Answer
Yes, the answers agree.
Work Step by Step
Product Rule:
$f(x)=(1+2x^2)(x-x^2)$
$f'(x)=(1+2x^2)(1-2x)+(x-x^2)(0+4x)$
$f'(x)=(1-2x+2x^2-4x^3)+(4x^2-4x^3)$
$f'(x)=-8x^3+6x^2-2x+1$
Performing Multiplication First:
$f(x)=(1+2x^2)(x-x^2)$
$f(x)=x-x^2+2x^3-2x^4$
$f'(x)=1-2x+6x^2-8x^3=-8x^3+6x^2-2x+1$
Therefore, the answers agree.
