'Subs' is not defined error when trying to graph the tangent line of the derivative of my function

I’ve graphed my original function and I want to graph the tangent line at the point of interest.

import numpy as np
from sympy import lambdify, symbols, diff, Abs

point_of_interest = 8
graphRange = [1,15]

# define the variable and the function
xsym = symbols('x')

# With a chord length of 60, plot the circle diameters
origFunction = 2 * ((60 ** 2) / (8 * Abs(xsym)) + Abs(xsym) / 2)

# define the derivative
derivative = diff(origFunction, xsym)

# define the tangent line at point of interest
tangentLine = derivative.subs(xsym, point_of_interest) * (xsym - point_of_interest) + origFunction.subs(xsym, point_of_interest)

# Convert the SymPy function to a lambda function
origF = lambdify(xsym, origFunction, "numpy")

# Generate x values
x_values = np.linspace(graphRange[0], graphRange[1], 100)

# Generate y-values for the original function
y_values = origF(x_values)

# Plot the original function
plt.plot(x_values, y_values, label='Original Function')

# THIS SECTION DOESN'T WORK YET
# Convert the SymPy function to a lambda function
diffF = lambdify(xsym, tangentLine, "numpy")

# Generate y-values for the tangent line
y_tang_values = diffF(x_values)

# Plot the tangent line
plt.plot(x_values, y_tang_values, label='Tangent Line')

#plot the point of interest
plt.plot(point_of_interest, origF(point_of_interest), 'ro', label='Point of Interest')

# Add labels and legend
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of Original Function and Tangent Line')
plt.legend()

# Show the plot
plt.show()

The error I get is this

Traceback (most recent call last):
File "x:\Python Projects\Chord calc.py", line 37, in
y_tang_values = diffF(x_values)
^^^^^^^^^^^^^^^
File "", line 4, in _lambdifygenerated
NameError: name ‘Subs’ is not defined

I don’t know what to do to fix this error.

>Solution :

At the moment, you are using a complex symbol, xsym: it doesn’t have any assumptions, hence it is as general as it gets.

Your function contains Abs(xsym): because xsym is complex, its derivative will be quite convoluted:

print(Abs(xsym).diff(xsym))
# (re(x)*Derivative(re(x), x) + im(x)*Derivative(im(x), x))*sign(x)/x

Once you substitutes a numeric value into that expression, Subs appears, and you get the error later on.

The solution is simple: create a real symbol. Replace this line:

xsym = symbols('x')

with:

xsym = symbols('x', real=True)

Then, everything will work as expected.