Using the quotient rule, which is

d/dx f(x)/g(x) = [g(x)f '(x) - f(x)g'(x)]/g(x)^2

f(u) = ln(u)/1 + ln(2u)

=> f '(u) = {[1 + ln(2u)](1/u) - ln(u)[1/u]}/(1 + ln(2u))^2

=> f '(u) = {(1 + ln(2u) - ln(u))/u}/(1 + ln(u))^2

=> f '(u) = [1 + ln(2u) - ln(u)]/u(1 + ln(u))^2

=> f '(u) = [1 + ln2]/u(1 + ln(u))^2 ........................we got to this step by combining the ln's. remember, lnx - lny = ln(x/y)

where did you make the mistake? first off, the derivative of ln(2u) is 1/u by the chain rule. if this was not your fatal mistake, perhaps you used the quotient rule incorrectly