Originally Posted by

**JeffM** You need to remember the basic idea behind elementary algebra: letters and expressions just represent numbers.

$5 * 2^2 * 3 = 5 * 4 * 3 = 60 \ne (5 * 2^2) * (5 * 3) = 20 * 15 = 300.$

However, I think I know what is bothering you with respect to the differentiation. This problem requires you to use the chain rule (at least implicitly) in addition to the product and power rules. In my opinion, until you hum at differentiating, it is best to use the chain rule explicitly.

$y = 9(2x^2 - 4x + 5)^8(4x - 4)\ and\ w = (2x^2 - 4x + 5)^8(4x - 4) \implies$

$ y = 9w \implies \dfrac{dy}{dw} = 9 \implies \dfrac{dy}{dx} = \dfrac{dy}{dw} * \dfrac{dw}{dx} = 9 * \dfrac{dw}{dx}.$

Now you know what to do with the 9. All you have left to do is to deal with $(2x^2 - 4x + 5)^8(4x - 4).$

Personally I'd recommend using the chain rule explicitly some more if you have any uncertainty. Hope this helps. If not, ask a follow up question.