Answer
$f'(x)=7x^6+6x^5+4x^3-9x^2-4x+2$
Work Step by Step
Product Rule:
$f′(x)=((u(x)(v(x)w(x))′=u′(x)v(x)w(x)+u(x)v′(x)w(x)$
$+u(x)v(x)w′(x)$
$u(x)=(x^3-x);u′(x)=(3x^2-1)$
$v(x)=(x^2+2);v′(x)=2x$
$w(x)=(x^2+x-1);w′(x)=(2x+1)$
$f'(x)=(3x^2-1)(x^2+2)(x^2+x-1)+$
$(x^3-x)(2x)(x^2+x-1)+(x^3-x)(x^2+2)(2x+1)=$
$3x^6+5x^4−2x^2+3x^5+5x^3−2x−3x^4−5x^2+2+2x^6$
$−2x^4+2x^5−2x^3−2x^4+2x^2+2x^6+2x^4−4x^2+x^5+x^3$
$−2x=7x^6+6x^5+4x^3-9x^2-4x+2$
