Let f(x)= lim_n → ∞ Σ_r =0^n ((tan (x / 2^r+1)+ tan^3(x / 2^r+1))/(1- tan^2(x / 2^r+1))). Then lim_x → 0 (e^x- e^f(x))/((x-f(x))) is equal to ____.

Let $\displaystyle f(x)=\lim _{\mathrm{n} \rightarrow \infty} \sum_{\mathrm{r}=0}^{\mathrm{n}}\left(\frac{\tan \left(x / 2^{r+1}\right)+\tan ^3\left(x / 2^{r+1}\right)}{1-\tan ^2\left(x / 2^{r+1}\right)}\right)$. Then $\displaystyle \lim _{x \rightarrow 0} \frac{\mathrm{e}^x-\mathrm{e}^{f(x)}}{(x-f(x))}$ is equal to $\displaystyle \_\_\_\_$.