import sympy as sp

import numpy as np

import matplotlib.pylab as plt

x, v = sp.symbols('x v')

f = sp.Function('f')(x, v)

expr = -x - v

f = sp.lambdify((x, v), expr)

x = np.linspace(-1, 1, 10)

v = np.linspace(-1, 1, 10)

x, v = np.meshgrid(x, v)

result = f(x, v)

scale = np.sqrt(1 / (v ** 2 + result ** 2))

plt.quiver(x, v, v * scale, result * scale)

plt.show()