Answer
$f''(x)=432x^7+2160x^4+1728x.$
Work Step by Step
Using the Chain Rule:
$f'(x)=(6)(3x^2)(3)(x^3+4)^{3-1}=54x^2(x^3+4)^2$.
Using the Product Rule and the Chain Rule:
Product Rule $(f'’(x)=(u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$
$u(x)=54x^2 ;u’(x)= 108x$
$v(x)= (x^3+4)^2;v’(x)=6x^2(x^3+4) $
$f''(x)=(108x)(x^3+4)^2+(54x^2)(6x^2(x^3+4))$
$=432x^7+2160x^4+1728x$.
