# Parials and Derivatives

1. Feb 11, 2009

### Diffy

Is it possible to have a function that has bounded paritial derivatives, but is not differential? Can you give me an example? And if possible explain how this is possible?

I am having trouble understanding this calculus concept. Thanks.

2. Feb 12, 2009

### CompuChip

I assume that you meant "differentiable" instead of "differential"?

How about f(x) = |x|.
For all x, $$|f'(x)| \le 1$$
however, f(x) is not differentiable.

The boundedness of partial derivatives and differentiability don't have much to do with each other. On the other hand, for example, the derivative of f(x) = x2 is unbounded although f(x) is perfectly well differentiable (infinitely often, even).