math-derivatives.py

# Calculate the derivatives of the curve-fitting functions
# using SymPy, the symbolic computer algebra framework

from sympy import Eq, diff, exp, init_printing, log, pprint, simplify, symbols
from sympy.abc import a, b, c, t
init_printing()

print("Exponential Growth")

E = a * (1 + b) ** t
lE = simplify(log(E))

print(" ", "log ", symbols("E"), "=", lE)
print(" ", symbols("e1"), "=", simplify(diff(lE, a)))
print(" ", symbols("e2"), "=", simplify(diff(lE, b)))

print("")

print("Logistic Growth")

L = c / (1 + exp(-(t - b) / a))
lL = simplify(log(L))

print(" ", "log", symbols("L"), "=", lL)
print(" ", symbols("l1"), "=", simplify(diff(lL, a)))
print(" ", symbols("l2"), "=", simplify(diff(lL, b)))
print(" ", symbols("l3"), "=", simplify(diff(lL, c)))