## Calculus 10th Edition

$f''(x)=432x^7+2160x^4+1728x.$
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 $(f'’(x)=(u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=54x^2 ;u’(x)= 108x$ $v(x)= (x^3+4)^2;v’(x)=6x^2(x^3+4)$ $f''(x)=(108x)(x^3+4)^2+(54x^2)(6x^2(x^3+4))$ $=432x^7+2160x^4+1728x$.