If $f\left(x\right)=\prod _{n=1}^{100}{\left(x-n\right)}^{n\left(101-n\right)}$, where $\prod _{i=1}^k{a}_i$ stands for product $a_1.a_2..........a_k, \mathrm{then} \frac{f\left(101\right)}{f\text{'}\left(101\right)}=$
(A) 5050                  (B) $\frac{1}{5050}$                  (C) 10010                     (D) $\frac{1}{10010}$