We are supposed to differentiate the given function and simplify the answer. I'm not sure if I did this correctly.

F(x) = (1-2x)^2/(3x+1)^3

I proceeded this way:

(3x+1)^3(2)(1-2x) - (1-2x)^2(3)(3x+1)^2(3)=

(3x+1)^2(1-2x)[2(3x+1)-9(1-2x)] =

(3x+1)^2(1-2x)[(6x+2)-(9-18x)]

(3x+1)^2(1-2x)(24x-7)