# Is an everywhere differentiable function locally Lipschitz? [closed]

If we have a differentiable function $f:\mathbb{R}^n \to \mathbb{R}^n$, does it have to be locally Lipschitz? It's obviously true for continuously differentiable functions, but what happens without that assumption?

• What about stuff like $x^2\sin(1/x^2)$? – zhw. Apr 17 '15 at 21:52