See http://meta.math.stackexchange.com/q/21259/23353 for discussion

RepPowerLaw.py

import csv
import matplotlib.pyplot as plt
from math import log

def make_plot(x, y, xmin=0, ymin=0, xmax=None, ymax=None, xlabel='X', ylabel='Y'):
  # clear the figure
  plt.clf() 

  if xmax is None:
    xmax = max(x)
  if ymax is None:
    ymax = max(y)

  plt.xlabel(xlabel)
  plt.ylabel(ylabel)
  plt.ylim(ymin, ymax)
  plt.xlim(xmin, xmax)
  plt.plot(x, y)
  plt.show()

  return


if __name__ == '__main__':  
  repX  = []
  userY = []
  
  # Read in the CSV file
  with open('RepPowerLaw.csv', newline='') as csvfile:
    csvreader = csv.reader(csvfile)
    next(csvreader)
    for row in csvreader:
      repX.append(float(row[0]))
      userY.append(float(row[1]))

  # Compute discrete derivative at x midpoint between the samples above
  diffY = [ (userY[i+1]-userY[i])/(repX[i+1] - repX[i]) for i in range(len(userY) - 1)]
  midX = [ (repX[i+1]+repX[i])/2 for i in range(len(userY) - 1)]
  
  # Log plot values
  logDiffY = [log(x) for x in diffY]
  logMidX = [log(x) for x in midX]
  
  # Do three plots
  make_plot(repX, userY, xmax=8000, ymax=250000,
            xlabel = '$R$', ylabel = '$U$')

  make_plot(midX, diffY, xmax = 1000, ymax = 2000, 
            xlabel = '$R$', ylabel = '$dU/dR$')

  make_plot(logMidX, logDiffY, xmin=min(logMidX), ymin=min(logDiffY), 
            xlabel = '$\log(R)$', ylabel = '$\log(dU/dR)$')