Question

求隐函数的二阶导数答案是（x+y)/(x-y)

Answer 1

两边对x求导：

(2x-2yy')/(x²-y²)=[2(xy'-y)/x²]/(1+y²/x²)

(x-yy')/(x²-y²)=(xy'-y)/(x²+y²)

解出y‘即可

如果答案是（x+y)/(x-y),题目有印刷错误

题目是：ln(x^2+y^2)=2arctan(y/x)

(x+yy')/(x²+y²)=(xy'-y)/(x²+y²)

x+yy'=xy'-y

x+y=(x-y)y'

y'=（x+y)/(x-y)