#### Answer

$f'(x)=3x^{2}-6x+4$

#### Work Step by Step

Original Function
$f(x)=(x-3)(x^{2}+4)$
Apply the product rule: $f(x)g'(x)+g(x)f'(x)$
$f'(x)=(x-3)(2x)+(x^{2}+4)(1)$
Distributed
$f'(x)=2x^{2}-6x+x^{2}+4$
Simply and you get the answer
$f'(x)=3x^{2}-6x+4$