Let \(\displaystyle f(x)=\lim_{n\to\infty}\sum_{r=0}^{n}\left(\dfrac{\tan\left(\frac{x}{2^{r+1}}\right)+\tan^{3}\left(\frac{x}{2^{r+1}}\right)}{1-\tan^{2}\left(\frac{x}{2^{r+1}}\right)}\right) \). Then \(\displaystyle \lim_{x\to 0}\dfrac{e^{x}-e^{f(x)}}{(x-f(x))} \) is equal to __________________.
