## Calculus 8th Edition

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.