Answer
$f'(x)=15x^4+8x^3+21x^2+16x-20$
$f'(0)=-20$
Work Step by Step
Product Rule $f'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$
$u(x)=x^3+4x ;u’(x)=3x^2+4 $
$v(x)=(3x^2+2x-5) ;v’(x)=(6x+2) $
$f'(x)=(3x^2+4)(3x^2+2x-5)+(x^3+4x)(6x+2)=$
$(9x^4+6x^3-15x^2+12x^2+8x-20)+(6x^4+24x^2+2x^3+8x)=$
$15x^4+8x^3+21x^2+16x-20$
$f'(0)=15(0)^4+8(0)^3+21(0)^2+16(0)-20=-20$
