Sample-and-Hold Differentiator

Sounds like a job for Finite-Impulse-Response filter - more than two samples and a more complicated sum-and-difference of rather more numerous samples.

Differentiation automatically emphasises high frequency noise. With only two samples there's not a lot you can do to temper that, but a longer string of samples offers more room to play.

Don't you have to do it digitally then? What does zero hertz mean here - a second, a day, a year?

Oh, that's the easy part: if your signal is known to be bounded (like, less than 50 kV), then its derivative at zero Hertz is

|D(0)| < (50 kV) * (0) *2*pi

If you get any other answer than zero, that's quantization noise.

Any modulation that can be converted to a current, with a nearly-ideal capacitor, makes an integrator. Many op amps have no problem with currents in the nanoamp range, and capacitors at 1 uF are available with low leakage, so times up to ten thousand seconds are no problem for analog hardware.

I'd try something like this.

.-[R1]-. | | C1 | |\ | in --||-+-|-\ | | >-+---- out .---|+/ | |/ | -+- 0V

That has a noise crisis. Add a resistor in series with C1.

Or

in-------C1----+--------out | | R1 | | gnd