To calculate the derivative of a function f at a given point x, a solution with python is to use the scipy function called derivative. Let's consider the following function: $f(x)=x^2$ quand x=2.

`>>> from scipy import misc`

`>>>`

`>>> def fonction(x):`

`... return x*x`

`...`

`>>> misc.derivative(fonction, 2.0)`

`4.0`

First, the misc module is imported with the command "from scipy import misc" and then a simple function is defined that return here the value of f for a given x:

`def fonction(x):`

`return x*x`

To get the value of the derivative of f at a given x, the function misc.derivative(fonction, x) can then be used.

It is then possible to extend this simple example and to plot the result using matplotlib:

`from pylab import *`

`from scipy import misc`

`ax = subplot(111)`

`def fonction(x):`

`return 3*x*x+2*x+1`

`x = arange(-2.0, 2.0, 0.01)`

`y = fonction(x)`

`plot(x, y,'r-')`

`yp = misc.derivative(fonction, x)`

`plot(x, yp,'b-')`

`grid(True)`

`ax.spines['left'].set_position('zero')`

`ax.spines['right'].set_color('none')`

`ax.spines['bottom'].set_position('zero')`

`ax.spines['top'].set_color('none')`

`text(-0.75, 6.0,`

`r'$f(x)=3x^2+2x+1$', horizontalalignment='center',`

`fontsize=18,color='red')`

`text(-1.0, -8.0,`

`r"$f'(x)=6x+2$", horizontalalignment='center',`

`fontsize=18,color='blue')`

`show()`