I have never seen the use of Parks-Mcclellan for differentiator - most uses tend to be lowpass filters. Is this because Parks-Mcclellan implementation of FIR differentiator has numerical problems and cannot be successful?
It seems though that Parks-Mcclellan for a differentiator should be more studied and obvious, because in terms of fit of a function, a differentiator has frequency response that is basically a sloped straight line or an identity function.
In general, I am having some difficulty finding established optimal ways to implement FIR differentiators. Are there other known ways that are commonly used for FIR differentiators? What about lowpass differentiators, where frequency response basically is a differentiator up to some frequency and from some frequency to $\pi$ it is filtered out, with transition band in the middle?