<s>[INST] Find ${\rm d}y/{\rm d}x$ and simplify as much as possible, $y=x/(2x+5)^3$ My answer is $-6x(2x+5)^2+(2x+5)^{-3}$. I am wondering if my answer is right and whether I am able to simplify more? 
 [/INST] You can use the quotient rule directly: $$\frac{{\rm d}y}{{\rm d}x} = \frac{(2x+5)^3-6x(2x+5)^2}{(2x+5)^6} = \frac{2x+5-6x}{(2x+5)^4} = \frac{-4x+5}{(2x+5)^4}.$$
This in fact indicates that you've got a little mistake: it's $(2x+5)^{-4}$ instead of $(2x+5)^2$ in what you have written there. I, particularly, prefer to leave stuff in a single fraction. 

Another approach: writing $y = x(2x+5)^{-3}$ and using the product rule, we have: $$\frac{{\rm d}y}{{\rm d}x} = (2x+5)^{-3} - x(-3(2x+5)^{-4}2) = (2x+5)^{-3}-6x(2x+5)^{-4}.$$
Your mistake probably was thinking that $(({\rm stuff})^{-3})'  = -3({\rm stuff})^{-2}$, because $2 < 3$, and also a sign mistake. You decrease the exponent, so $-3 \to -4$.
</s>