Derivative

Let $f:\mathbb {Q} \rightarrow \mathbb {Q}$, and let $\epsilon :\mathbb {Q}$ be positive. We define $\Delta _{\epsilon }f:\mathbb {Q} \rightarrow \mathbb {Q}$ by

$$(\Delta _{\epsilon }f)(x):={\frac {f(x+\epsilon )-f(x)}{\epsilon }}.$$

We say that $f$ is differentiable if is .... nill whenever