Chain Rule and Product Rule Question

I haven't taken a math course in two years and I have a hard time with some simple things.

3(x^2-2)^4 For this problem we would just do the Chain Rule. The answer would be 24x(x^2-2)^3

x(4-3)^3 Here we are supposed to do the Product Rule first, then the Chain Rule and the answer should be 4(4-x)^2(1-x)

Why is it in the first problem the product rule is not necessary? Is it because the second problem there is a "X" in front? Why do we do the product rule first for the "X" but not for the "3"?

Re: Chain Rule and Product Rule Question

because $\displaystyle \frac{d}{dx} k \cdot f(x) = k \cdot f'(x)$ , for any **constant** $\displaystyle k$