Plotting Functions With Sympy

import matplotlib.pyplot as plt
from sympy import tan, exp, plot, symbols, log, latex

This is a function for plotting mathmetical functions

In [2]:

def plot_functions(f,
                   g = None,
                   show = False,
                   diff_plot = False,
                   xlim = (-10, 10),
                   ylim = (-10, 10),
                   color = ['r', 'm', 'b', 'g']):
    x = symbols('x')
    if g is None:
        p1 = plot(f(x), (x, xlim[0], xlim[1]),
                  show = False,
                  line_color = color[0],
                  ylim = ylim,
                  label = f'${latex(f(x))}$',
                  legend  = True)
        if diff_plot:
            p2 = plot(f(x).diff(), (x, xlim[0], xlim[1]),
                      show = False,
                      line_color = color[1],
                      ylim = ylim,
                      label = f'${latex(f(x).diff()}$',
                      legend  = True)
            p1.extend(p2)
        if show:
            p1.show()
            return p1
p1 = plot(f(x), (x, xlim[0], xlim[1]),
              show = False,
              line_color = color[0],
              ylim = ylim,
              label = f'${latex(f(x))}$',
              legend  = True)
    p2 = plot(g(x), (x, xlim[0], xlim[1]),
              show = False,
              line_color = color[1],
              ylim = ylim,
              label = f'${latex(g(x))}$',
              legend  = True)
    p1.extend(p2)
        if diff_plot:
            p1_diff = plot(f(x).diff(), (x, xlim[0], xlim[1]),
                      show = False,
                      line_color = color[2],
                      ylim = ylim,
                      label = f'${latex(f(x).diff()}$',
                      legend  = True)
            p1.extend(p1_diff)
            p2_diff = plot(g(x).diff(), (x, xlim[0], xlim[1]),
                      show = False,
                      line_color = color[3],
                      ylim = ylim,
                      label = f'${latex(g(x).diff()}$',
                      legend  = True)
            p1.extend(p2_diff)
    ​if show:
        p1.show()
    return p1

Creating a symbol x

In [3]:

x = symbols('x')

Now, we can plot any function.

In this we are plotting the tan function

In [4]:

f = lambda x: tan(x)
plot_functions(f, show = True)

Plotting the Log function with its derivative.

In [5]:

f = lambda x: log(x)
plot_functions(f, show = True, diff_plot = True

Comparing two functions, log and exp. (with its derivative)

In [6]:

f = lambda x: log(x)
g = lambda x: exp(x)
plot_functions(f, g, show = True, diff_plot = True)

Which function has more rate of change, x ** 2 or 2 ** x?

In [7]:

f = lambda x: x**2
g = lambda x: 2**x
plot_functions(f, g, ylim = [0, 1000], show = True)

As you can see the function 2 ** x has very high rate of change.

In [8]:

f = lambda x: x**2
g = lambda x: 2**x
plot_functions(f, g, ylim = [0, 1000], diff_plot = True, show = True)