Question

求隐函数x²–y²=0的二阶导数

Answer 1

求隐函数x^2-y^2=0的二阶导数
x^2-y^2=0
两边求导
2x-2y.y'=0
y'=x/y
两边求导
y''
=(y-xy')/y^2
=[y-x(x/y)]/y^2
=(y^2-x^2)/y^3
得出结果
y''=(y^2-x^2)/y^3

Answer 2

x²–y²=0
2x - 2yy' = 0
y' = x/y
y'' = (y-xy')/y^2 = (y-x^2/y)/y^2 = (y^2-x^2)/y^3 = 0

Answer 3

设：F=x²–y²
则：∂F/∂x=2x
∂F/∂y=-2y
dy/dx=-(2x)/(-2y)=x/y
d²y/dx²=(y-xy')/y²=(y-x²/y)/y²=(y²-x²)/y³

Answer 4

x²-y²=0 ①
对①求导可得：2x-2yy′=0 ②，
2yy′=2x，
即 y′=x/y
对②求导
2-(2y′y′+2yy′′)=0
2-2(y′)²-yy′′=0
2-2(x/y)²=yy″
y″=(2y²-2x²)/y³