Cho hàm số f(x)= ln 2018x/ x + 1. Tính tổng S= f'(1) + f'(2) +..+ f'(2018)

Ta có:f(x)=ln2018xx+1⇒f'(x)=2018(x+1)22018xx+1=1x(x+1)=1x−1x+1

 ⇒f'(1)=11−12;f'(2)=12−13;...;f'(2018)=12018−12019 

Nên:S=f'(1)+f'(2)+...+f'(2018)

          =1−12+12−13+...+12018−12019=1−12019=20182019. 

Chọn A.