设方程3^（xy)=x+y+1确定的隐函数为y=y(x),求y'(0)._数学解答

设方程3^（xy)=x+y+1确定的隐函数为y=y(x),求y'(0).

人气：197 ℃　时间：2020-06-16 19:29:05

解答

两边对x求导:
[3^(xy)](xy)'ln3 = 1 + y'
(y + xy')[3^(xy)]ln3 = 1 + y'
x = 0, 3⁰ = 0 + y + 1, y = 0
(0 + 0*y')3⁰ln3 = 1 + y'
y' + 1 = 0
y' = -1