How to Measure differential conductance dI/dV experimentally?
There's many ways to measure it.

I assume you're interested in the differential resistance of a two-terminal device, or of a port on an n-port device.

You could use a semiconductor parameter analyzer to sweep voltage or current and measure the response, then take a numerical derivative.

You could use a function generator (possibly with a circuit to bias the device to the interesting operating point) to apply a sinusoidal voltage, and measure the current response.

You could use a vector network analyzer to measure the RF reflection coefficient at a particular bias point and determine the resistance from that.