import numpy as np
import scipy
from scipy.misc import derivative

x0 = 0.5
x1 = 0.55
x2 = 0.6
x3 = 0.65
x = 0.55


def def_func(x):
    return 2*x - (1)/((x+2)*np.log(10))

def func(x):
    return (x ** 2) - np.log10(x + 2)


def lagrange3(x):
    return func(x0) * (x - x1) * (x - x2) * (x - x3) / ((x0 - x1) * (x0 - x2) * (x0 - x3)) + \
           func(x1) * (x - x0) * (x - x2) * (x - x3) / ((x1 - x0) * (x1 - x2) * (x1 - x3)) + \
           func(x2) * (x - x0) * (x - x1) * (x - x3) / ((x2 - x0) * (x2 - x1) * (x2 - x3)) + \
           func(x3) * (x - x0) * (x - x1) * (x - x2) / ((x3 - x0) * (x3 - x1) * (x3 - x2))


def defferencial(x):
    return scipy.misc.derivative(lagrange3, x,
                                 dx=0.00000000001)


print(defferencial(x))
print(def_func(x))
r = def_func(x) - defferencial(x)
print(r)