Let's start by defining a function of one variable. We'll use NumPy to estimate the derivative numerically, and we'll plot the estimate with matplotlib.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
mpl.rc('font', size=10) # set default font size
dx = 0.01
x = np.arange(0, 2, dx)
f = power(x, 3)
dfdx = 3*power(x, 2)
plt.figure(figsize=(4, 4))
plt.plot(x, f, label='f(x)')
plt.plot(x, dfdx, color='red', label='Analytical df/dx')
df = np.diff(f)
plt.plot(x[:-1], df/dx, color='black', label='Numerical df/dx')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.legend(loc='best')
plt.savefig('diff.png')
plt.close()The output is shown in the following screenshot:
