## Calculus, 10th Edition (Anton)

A smooth curve must have a derivative that is continuous on an interval $[a,b]$. The derivative of $y$ is $$\frac{-2x}{\sqrt{1-x^{2}}}$$ This has an asymptote at both $x=1$ and $x=-1$, so the derivative cannot be continuous on $[-1,1]$ and the graph is not smooth.