I have attempted to come up with functions that are continuous and differentiable on an arbitrary interval $(-1, 1)$, but their derivative is not continuous on $(-1,1)$, ideally due to a division by zero in the denominator. Perhaps it is due to the time, or my ignorance, but I am failing at arriving at an example. This is a recommended practice problem for an upcoming exam, just so I'm transparent.
2026-04-07 16:16:29.1775578589
Finding an example of a function $f(x)$ that is differentiable on $(a,b)$ but $f'(x)$ is not continuous on $(a,b)$.
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