I am attempting to take the left derivative at 1 and the right derivative at -1 of the following function, $f(x): \operatorname{R} \rightarrow \operatorname{R}$
$$f(x) = \begin{cases} e^{\frac{1}{x^2-1}}, \text{if} \, |x|< 1, \\ 0, \text{if} \, |x| \geq 1. \end{cases}$$
The epsilon-delta statement for the right derivative should read that $\forall \epsilon > 0$, $\exists \delta > 0$ such that $\exp{\frac{1}{x^2 - 1}} \over {|x+1|}$ < $\epsilon$ if $-1 < x < \delta -1$, since the right derivative is 0.
When I've done other epsilon-delta problems, the numerator was of the form $|x+a|$, and the trick was to make a restriction on $|x+a|$, e.g., $|x+a| < 1$. Should I do the same here? Or is there a different way?