Electronic – Channel to bulk capacitance in inversion

As stated in the introduction, all other voltages are held constant:

Derivation: consider for example the relationship of the increment in drain current due to an increment in gate-source voltage when the MOSFET is saturated-- with all other voltages held constant.

An for this reason only the change of the gate-source voltage is considered.

Of course to extend this model a similar derivation will be done for vds and vbs resulting in gds and gmbs.

My answer is written as if dealing with a real circuit amplifier but the same principle is involved when calculating values.

You don't have to set the input source to zero if you want to do it the harder way.

That harder way would test the impedance at a specific frequency other than what the input source is producing then you would use a tight band-pass filter (or fourier/spectral analysis) to analyse JUST the signal at the frequency you want to measure and calculate output impedance.

Yes, you can do it that hard way or, just set the source voltage to zero and do it the easy way. Alternatively you can use the input signal to generate a voltage and then place a load at the drain/collector and when that AC voltage seen drops to 50% you have the equivalent of the output impedance.