bounded subset of $\mathcal{C}^1(\Omega)$ is precompact in $\mathcal{C}^0(\Omega)$

Question

I have to prove the following statement:

Assume that $\Omega$ is a open domain in $\mathbb{R}^N, N \in \mathbb{N}$. Let A be a bounded subset of $\mathcal{C}^1(\Omega)$ then A is precompact in $\mathcal{C}^0(\Omega)$.

Because every sequence in $\mathcal{C}^0(\Omega)$ has to be bounded, I thought about proving the statement in a similar way to the theorem of Bolzano Weierstrass, but I'm not sure how or if that works.

Any kind of help would be appreciated.