How to use a global variable (derivative expression) inside a function

This script works perfectly for what I want. It is a weight function that I want to minimize. I wrote inside a function and globally and I noticed that the global print(W) is my expression and the print(W) inside the function is the array of values to be plotted:

import numpy as np
from sympy import *
import matplotlib.pyplot as plt

#Weight function

tf = Symbol('tf')
l = 50/(0.54*tf) - tf
d = (tf*(2*l+2*(l-tf)/2))/(2*l*(l+tf)/2)
W = 15.7*tf-7.85*tf*d+7.85*d*50/(0.54*tf)
print(W)

def func(tf):
    l = 50/(0.54*tf) - tf
    d = (tf*(2*l+2*(l-tf)/2))/(2*l*(l+tf)/2)
    W = 15.7*tf-7.85*tf*d+7.85*d*50/(0.54*tf)
    print(W)
    return W

b = np.linspace(1, 10, 201)
plt.plot(b, func(b))
plt.xlabel("tf", fontsize=18)
plt.ylabel("Weight", fontsize=18)
plt.grid()
plt.show()

My problem happens now. I want the weight function derivative plotted as well. But I can't do it inside the function because it recognizes as a number (first element of the array). The first print gives me the expression I want to plot but I cannot send that expression inside the function. How can I call a global variable (derivative expression) to be used inside the function?

dW_dtf = W.diff(tf)
print(dW_dtf)

def funcd(tf):
    l = M/(a*tf) - tf
    tw = tf
    d = (tw*(2*l+2*(l-tw)/2))/(2*l*(l+tw)/2)
    W = 15.7*tf-7.85*tf*d+7.85*d*M/(a*tf)
    dW_dtf = W.diff(tf)
    return dW_dtf

AttributeError: 'numpy.ndarray' object has no attribute 'diff'

I'm open to other options to do what I want. I will be reading more about optimization algorithms using python because I will have to solve more difficult problems but I would like to make this kind of basic problems without using iterative methods. Thank you. Luis

Solution

In your code, you are essentially overriding your global definition. Right now, when you call func, you redefine W using whatever value you submitted as tf. In your case, an array. In that way, W is no longer a symbolic expression but plainly an array. What you want is something like this instead of func:

def func(x):
    w_evaluator=lambdify(tf,W)
    return w_evaluator(x)

And analogously:

def funcd(x):
     dwdt_evaluator=lambdify(tf,W.diff(tf))
     return dwdt_evaluator(x)