It is a well-known theorem that if $f:\mathbb{R}\to\mathbb{R}$ is a differentiable function such that $f'(t)=0$ for all $t\in\mathbb{R}$, then $f$ is constant.

Is it true that if $f:\mathbb{Q}\to\mathbb{Q}$ is a differentiable function such that $f'(t)=0$ for all $t\in\mathbb{Q}$, then $f$ is constant?

**Notations**:

- $\mathbb R$ denotes the set of real numbers.
- $\mathbb Q$ denotes the set of rational numbers.

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