I was reading wiki and found this statement. Quoting it:
A function f is said to be continuously differentiable if the derivative f'(x) exists and is itself a continuous function. Though the derivative of a differentiable function never has a jump discontinuity, it is possible for the derivative to have an essential discontinuity.
I am confused with this statement as we know :
Function is differentiable in its domain -> continuous in that domain
Not continuous -> Not differentiable
How does a function still be differentiable even if it is not continuous ?
How It can have essential discontinuity ? I did not get it from wiki example.
Please clarify :)