Find the derivative of 200(q+1)/(q+2)^2. Which of the following options correctly represents the derivative of the given expression?

A) 200(q+2)/(q+2)^2
B) 200(q+1)/(q+2)
C) 200(q+1)/(q+2)^3
D) 200(q+2)/(q+2)^3