- is differentiable on the open interval ;
- is differentiable on the right at ;
- is differentiable on the left at .

There are similar definitions for other intervals, like , etc.

For , .

Hence, the square root function is differentiable on .

Take now . Then:

The square root function is not differentiable on the right at 0.

Noah Dana-Picard 2007-12-28