Help clarifying the steps to find the derivative of $y=(3x+1)^3(2x+5)^{-4}$ For the problem $y=(3x+1)^3(2x+5)^{-4}$ do I use the chain, quotient and product rules? If so how do I know what parts to break up and where the rules apply?   For instance would I consider $f(x)$ to be $(3x+1)^3$ and $g(x)$ to be $(2x+5)^{-4}$? If so do I then need to take the product rule of $f(x)$ and the quotient of $g(x)$ and then combine them? Or do I just use one rule?

there is:
$$\left(\frac{u}{v}\right)' = \frac{u'v-uv'}{v^2}$$
your example can be rewritten like:
$$\frac{(3x+1)^3}{(2x+5)^4}$$
and therefore:
$$\frac{9(3x+1)^2\cdot (2x+5)^4-(3x+1)^3\cdot8(2x+5)^3}{(2x+5)^8}$$
