As has been stated, the differential function effectively amplifes 'noise', in particular white noise.
The numerical differetial of a data set (rather than the analystic differential of a function) is essentially a finite impulse response filter. That is you select a few data points around the desired point of differentiation, and then weight them and add them (some weights being negative). Thus you get to choose the effective filter response, and cutoff, of the differential.
If the data is not uniformly spaced, you can adjust the weightings to match the spacings, etc.
For your solar cell case, you have two options (approaches), one is to presume that the physics that others have already taught is true and you are just fitting parameters, the other is think that your cell is different/special and you need to create a model from the data.
The usual result is to start with option one (parameter fit to known model) then to look at the deviations of the data from the model and to try and explain then with additional elements in the model. These additional elements may be limitations of the test set (e.g. lead resistances), Knowledge limitations (photo response curves being a potentially big error here), or finesse of the finer details of the solar cell's internal models (two photon conversion?, etc.)
So, in summary, given a noisy data set, you can design a diferential filter with known selectivity.
Philip Oakley
