# Is this function infinitely differentiable?

Let $$f(x)=\begin{cases}\exp\left(1-\frac{1}{1-|x|}\right),\,\,&|x|<1\\0,&\text{otherwise}.\end{cases}$$ and show that $$f$$ is continuously differentiable.

I took the derivative and obtained $$f'(x)=\begin{cases}\frac{\text{sgn}(x)}{(1-|x|)^2}\exp\left(1-\frac{1}{1-|x|}\right),\,\,&|x|<1\\0,&\text{otherwise}.\end{cases}$$ which does not look to be continous at $$x=0$$ and thus is not continuously differentiable. Did I do something wrong?