example of a non differentiable manifold

example of a non differentiable manifold

Take the manifold: The graph of $|x|$ on $(-1,1)$, with the induced
topology from $\mathbb{R}^2$. This is a topological manifold, which is
homeomorphic to $(-1,1)$ by projection. Is it a differentiable manifold? I
believe it is, because we can take an atlas with only the projection, and
then we will have only one transition map which is the identity, and
therefore differentiable. But I'm not sure I get the definition of a
differentiable manifold right...
Thanks!