用sympy求隐函数二阶导数

implicit_func_2nd_diff.py

from sympy import symbols, Function, Eq,log,solve, simplify

def derivative_hidden_function(equation, x, y_func,N):
    # 对方程关于 x 求导，使用链式法则
    diff_eq = equation.lhs.diff(x) - equation.rhs.diff(x)
    # 解出 dy/dx
    dy_dx = solve(diff_eq, y_func.diff(x))[0]
    if N==1:
        return dy_dx
    diy_dxi=dy_dx
    # 对 dy/dx 关于 x 求导，使用链式法则
    for i in range(N-1):
        diy_dxi = diy_dxi.diff(x).subs(y_func.diff(x), dy_dx)
        diy_dxi = simplify(diy_dxi)
    return simplify(diy_dxi)

# 定义 x 和 y 为符号变量
x = symbols('x')
y = symbols('y', cls=Function)
y = y(x)

# 示例方程
example_equation = Eq(y-2*x, (x-y)*log(x-y))

# 调用函数并显示结果
derivative_hidden_function(example_equation, x, y,3)

这里的关键是要声明y是函数，y=y(x)
y = symbols('y', cls=Function)
y = y(x)

更新成对隐函数求N阶导数了。
更详细的说明请参考
https://quail.ink/goldengrape/p/using-wolfram-language-and-python-to-calculate-implicit-function-derivatives#pythonn