According to the definition, we need the limit of the function when alpha
approaches 0. How to implement this on a Function object?
from sympy import *
from sympy.abc import *
from IPython.display import display
init_printing(use_latex='mathjax')
def func_diff(F, f, df):
alpha = Symbol('alpha')
F = F.subs(f, f+alpha*df)
dF = F.diff(alpha)
return simplify(dF.subs(alpha, 0))
u = Function('u')(x,y,z)
du = Function('\delta u')(x,y,z)
dfun = func_diff(u**2, u, du)
display(dfun)
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