Obviously we can "brute force" this by multiplying the various terms and differentiating from there. But based upon the solution provided in the text where I found this problem, it looks like there's a "cleaner" method available.
Of note, this problem appears in the chapter introducing the chain rule.
Any ideas?
UPDATE: just to clarify, this problem appears in a very basic calculus text, so any/all "advanced" differentiation techniques would not be at the student's disposal. It's also worth pointing out the answer provided in the text:
$2(x + 2)(x + 3)^2(3x^2 + 11x + 9)$