Getting rid of noise in derivative?

[jadi929]

Hey guys, I'm working on some Current-Voltage data in excel. I need to do some analysis with the data, and the first step is to compute dV/dI. I have to do this in excel so decided to use excel's SLOPE function (5 point slope) to compute dV/dI. However, it seems that the derivative has a lot of noise, especially towards the lower values. Since I am writing a program to automate this analysis, I would really like to get rid of this noise.

Another way I thought of was to fit a line to my initial data, and simply differentiate the fitted line's equation. However, I can't seem to get a decent fit for my initial curve.

Pic shows the initial data and my horrible looking derivative.

screenshot app

 

[Stephen Tashi]

If you want a mathematically defensible way to smooth the derivative then you need to explain the nature of the "noise". in the data - e.g. can it be modeled as an independent random error at each measurement?

Another thing to try is a "multi-point method" for estimating the derivative. For example, see the "Higher-order methods" section of http://en.wikipedia.org/wiki/Numerical_differentiation. (However, I don't know if that method has any "noise cancelation" properties.)

If you only want a nice pitcure, Is there some reason that you can't fit a smooth function to the data first and then plot the derivative of that function?