Let $f_n: [0, 1] \to \mathbb R$ be a sequence of continuously differentiable functions. We say that the sequence $f_n$ is *equidifferentiable* if for every $x \in [0, 1]$ and every $\varepsilon > 0$, there exists a $\delta > 0$ such that for all $n \in \mathbb N$,

$$\frac{|f_n (x) - f_n (y) - f_n’(x)(x-y)|}{|x-y|} < \varepsilon$$

for all $y$ with $|x - y| < \delta$.

**Question:** Given a sequence $f_n$ of continuously differentiable functions, is it true that $f_n$ are equidifferentiable if and only if the sequence $f’_n$ is equicontinuous?