使用Python计算偏导数

pip install sympy

from sympy import symbols, diff
 
# 定义变量和函数
x, y = symbols('x y')
f = x**2 + y**3
 
# 计算偏导数
df_dx = diff(f, x)
df_dy = diff(f, y)
 
# 打印结果
print("偏导数 df/dx:", df_dx)
print("偏导数 df/dy:", df_dy)

# 替换变量并计算具体值
x_value = 2
y_value = 3
 
result_dx = df_dx.subs({x: x_value, y: y_value})
result_dy = df_dy.subs({x: x_value, y: y_value})
 
print(f"在 x={x_value}, y={y_value} 处的偏导数 df/dx 的值为:", result_dx)
print(f"在 x={x_value}, y={y_value} 处的偏导数 df/dy 的值为:", result_dy)
np

pip install numpy

import numpy as np
 
# 定义函数
def f(x, y):
    return x**2 + y**3
 
# 定义计算偏导数的函数
def partial_derivative(func, var=0, point=[]):
    args = point[:]
    def wraps(x):
        args[var] = x
        return func(*args)
    return np.vectorize(wraps)
 
# 定义变量和计算点
x_value = 2
y_value = 3
 
# 计算偏导数
df_dx = partial_derivative(f, var=0, point=[x_value, y_value])
df_dy = partial_derivative(f, var=1, point=[x_value, y_value])
 
# 打印结果
print(f"在 x={x_value}, y={y_value} 处的偏导数 df/dx 的值为:", df_dx(x_value))
print(f"在 x={x_value}, y={y_value} 处的偏导数 df/dy 的值为:", df_dy(y_value))