from sympy import *

if __name__ == '__main__':
    # 函数表达式变量
    x, y = symbols('x y')

    # 二元函数表达式
    f = x ** 2 + 3 * x * y + y - 1

    # f关于x的偏导数,y是常量
    fx = diff(f, x)
    print(fx)

    # f关于y的偏导数,x是常量
    fy = diff(f, y)
    print(fy)

    result1 = fx.subs({x: 4, y: -5})
    print(result1)

    result2 = fy.subs([(x, 4), (y, -5)])
    print(result2)

    # 再来一例二元三角函数的偏导数
    # 求 f = y*sin(x*y)关于y的偏导数，x是常量
    print(diff(y * sin(x * y), y))

输出：

2*x + 3*y
3*x + 1
-7
13
x*y*cos(x*y) + sin(x*y)