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?

You can chain the rules together.  Each application of a rule gives you a simpler object to take the derivative of.  I would start by using the product rule, giving $$\frac {dy}{dx}=(2x+5)^{-4}\frac d{dx}\left((3x+1)^3\right)+(3x+1)^{3}\frac d{dx}\left((2x+5)^{-4}\right)$$
Now you can use the chain rule on each term, getting $$\frac d{dx}\left((3x+1)^3\right)=3(3x+1)^2\frac d{dx}(3x+1)$$
and similarly for the other term.  Probably you can do the last derivative on the right easily.  Then just gather it all together.  You could also use the quotient rule to start, but I find that a little more difficult.
