After learning about the use of ‘live integration’ for digital filters (brilliantly explained by Stephen here) I spontaneously wanted to create a live “derivator” - meaning a tool that repeatedly outputs the result of [ f( x ) -f( c ) ] / [c - x]

I have access to the value of f(a) since it’s my input. I also have the value of f(b) as this is simply the value of the input delayed by one sample. So far so good.

What I don’t understand is what the values of *c* and *x* should be. Since I’m doing this live, *x* is “now” and *c* is “1 sample ago”. I tried using x=0 and c=-1 but that seems foolish and it doesn’t work.

Maybe this stems from a poor understanding of the integrators in the first place. I don’t know. I think it can be musically useful to have access to the derivative of an LFO and I haven’t found this anywhere on the forum or Audulus resources.

Any pointers?

**edited with image.**