Johnson Noise in Differentiator: Does the input C have an effect?
Johnson Noise in Differentiator: Does the input C have an effect?

It can create a resonant point in the response. Here's a circuit that typically shows this (something I had previously set up): -

And, if I vary the value of the capacitor from 100 nF to 10 nF to 1 nF to 100 pF we see this (V3 is the input to the AC analysis): -

100 nF is the left side peak and 100 pF is the right side peak.
However, the peak is due to the op-amp not being ideal so, how you want to deal with this is down to you.