How do I plot the derivative of a set of experimental points?

Question

I have a set of points like this: P = {{$x_1$,$y_1$},{$x_2$,$y_2$},...,{$x_n$,$y_n$}}. I want to plot them and also plot the derivative of that graph. How can I do this with Mathematica? Is there a simple way in Mathematica?

Answer 1

Here is some sample data, hopefully of the sort you are looking for

a=Table[{i, i^2 - 3 i + 2 + 0.3 Random[]}, {i, -1, 3, 0.1}];
ListPlot[a]

will display the data.

This will create a derivable interpolation.

b = Interpolation[a, Method -> "Spline"];

This is its derivative

c = b';

Plot them together.

Plot[Evaluate[{b[x], c[x]}], {x, -1, 3}]

Answer 2

This is the data (taken from the previous example):

a = Table[{i, i^2 - 3 i + 2 + 0.3 Random[]}, {i, -1, 3, 0.1}];

This is derivatives calculated in each point except the first:

derA = Differences[a] /. {x_, y_} -> y/x;

here we combine it into the list of pairs:

lst=Transpose[{Drop[Transpose[a][[1]], 1], derA}];

Now we can plot it along with the initial list:

    ListLinePlot[{a, Transpose[{Drop[Transpose[a][[1]], 1], derA}]}, 
 PlotStyle -> {Blue, Red}]

That is what you get: