( $\dfrac{(x+2)^2}{(2x-1)^2}$ ) $'$ = $\dfrac{((x+2)^2)'(2x-1)^2-(x+2)^2.((2x-1)^2)'}{(2x-1)^4}$
= $\dfrac{2(x+2).(x+2)'.(2x-1)^2-(x+2)^2.2(2x-1).(2x-1)'}{(2x-1)^4}$
= $\dfrac{2(x+2).1.(2x-1)^2-(x+2)^2.2(2x-1).1}{(2x-1)^4}$
= $\dfrac{2(x+2).(2x-1)^2-(x+2)^2.2(2x-1)}{(2x-1)^4}$