For the structure $\mathcal M=(\mathbb R; +,-(), \cdot, \lt, 0,1,f), n_f=1 $ show that the set of all points $x \in \mathbb R$ where $f$ is differentiable is a definable set.
My issue here is how to write a formula $\phi$ for this structure describing differentiability at a point, when the definition uses the limit definition. Do I need to describe the limit in the formula using $\epsilon, \delta$? Wouldn't that produce an extremely long formula?
Any assistance will be great.