If $f(x)=\cos ^{-1}\left[\frac{1-(\log x)^2}{1+(\log x)^2}\right]$, then $f^{\prime}(e)=\ldots$

The value of $\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{7}+\tan ^{-1} \frac{1}{8}$ is ...........