problem recreating differentiator effect

The 1nF cap across the differentiator opamp is killing its response.

Without that, a pulse is produced, though at the time scale you are using it is very drawn out.

You are effectively trying to use the opamp at near infinite gain.

It's frequency response is drastically reduced for large signals and high gains - see figures 10 & 11 on page 6 of the datasheet:

The 100 Ohm load resistor is also below the minimum spec for that device.

What are you trying to use the PID for? In any application I've seen, the signal rates of change are typically very slow, or hundreds of Hz up to a few thousand Hz depending on the application - but not in the Megahertz range!

Design info attached :