Imagine I have a set of data, the plot is as following(just as an example consider a Gaussian curve): enter image description here

Is there any way to obtain the slop of this curve slop and plotted just using the initial data.

Thank alot

  • $\begingroup$ Do you have some example data? $\endgroup$ – Coolwater Jan 10 '18 at 15:39
  • $\begingroup$ And explain please, what is "the first plot in Mathematica"? $\endgroup$ – Alexei Boulbitch Jan 10 '18 at 15:46
  • $\begingroup$ @ Alexei Boulbitch I added an example, also by first data I meant the data I plotted the curve. $\endgroup$ – kmsin Jan 10 '18 at 15:54
  • $\begingroup$ @Coolwater I added an example. $\endgroup$ – kmsin Jan 10 '18 at 15:54
  • $\begingroup$ I want to plot the slop of this curve with his own data, is it possible? $\endgroup$ – kmsin Jan 10 '18 at 17:03

If you want to do it numerically with a dataset, say data

data = Table[{x, Exp[-x^2]}, {x, -5, 5, 0.1}];

you can go like this

ndata = Length[data];
slope = Table[{(data[[i, 1]] + data[[i - 1, 1]])/2, 
               (data[[i, 2]] - data[[i - 1, 2]])/(data[[i, 1]] - data[[i - 1, 1]]) },
              {i, 2, ndata}];
ListLinePlot[{data, slope}, PlotRange -> All]

enter image description here

Or you can go with Interpolation

f[x_] = Interpolation[data][x]; (*function for data*)
f1[x_] = D[f[x], x];            (*function for derivative*)
Plot[{f[x], f1[x]}, {x, -5, 5}]

enter image description here

  • $\begingroup$ Thanks, I was looking for something the same as the second part of your answer $\endgroup$ – kmsin Jan 10 '18 at 19:11
  • $\begingroup$ In case you know any trial function for your data, you can also use Fit, FindFit or NonlinearModelFit to find a functional form. $\endgroup$ – Sumit Jan 11 '18 at 17:04

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