title: Plotting the function 1/x and -1/x^2 on python in the interval from (-1,1)
body: <p>Please look at my code and help me.
  I'm writing a code the approximates the Derivative of a function. To visually check how close my approximation is with the real derivative, I'm plotting both of them together.</p>
  
  <p>My problem is when the function is not defined at zero, like 1/x with a derivative of '1/x^2.</p>
  
  <p>Thanks in advance.</p>
  
  <pre><code># -*- coding: utf-8 -*-
  from pylab import *
  import math
  def Derivative(f,x, Tol = 10e-5, Max = 20):
  try:
      k = 2
      D_old = (f(x+2.0**(-k))-f(x-2.0**-k))/(2.0**(1-k))
      k = 3
      D_new = (f(x+2.0**(-k))-f(x-2.0**-k))/(2.0**(1-k))
  
      E_old = abs(D_new - D_old)
  
      while True:
          D_old = D_new 
  
          k+=1
  
          D_new = (f(x+2.0**(-k))-f(x-2.0**-k))/(2.0**(1-k))
          E_new = abs(D_old - D_new)
  
          if E_new &lt; Tol or E_new &gt;= E_old or k &gt;= Max:
              return D_old
  
  except:
      return nan
  def Fa(x):
       return math.sin(2*math.pi*x)
  def Fap(x):
       return 2*math.pi*math.cos(2*math.pi*x)
  def Fb(x):
      return x**2
  def Fbp(x):
      return 2*x
  def Fc(x):
      return 1.0/x
  def Fcp(x):
      if abs(x)&lt;0.01:
      return 0
      else:
          return -1.0/x**2
  def Fd(x):
      return abs(x)
  def Fdp(x):
      return 1 #since it's x/sqrt(x**2)
  
  # Plot of Derivative Fa
  xx = arange(-1, 1, 0.01)              # A Numpy vector of x-values
  yy = [Derivative(Fa, x) for x in xx]  # Vector of f’ approximations
  plot(xx, yy, 'r--', linewidth = 5)      # solid red line of width 5
  
  yy2 = [Fap(x) for x in xx]
  plot(xx, yy2, 'b--', linewidth = 2)     # solid blue line of width 2
  
  # Plot of Derivative Fb
  
  yy = [Derivative(Fb, x) for x in xx]  # Vector of f’ approximations
  plot(xx, yy, 'g^', linewidth = 5)      # solid green line of width 5
  
  yy2 = [Fbp(x) for x in xx]
  plot(xx, yy2, 'y^', linewidth = 2)     # solid yellow line of width 2
  </code></pre>