Question

隐函数求导，求以下问题的答案，谢谢了，下面配有图？

做这种题的方法是什么？

Answer 1

两边取对数：

½ln(x²+y²)=arctan(y/x)

两过求导

½[(2x+2yy′)/(x²+y²)=[(xy′-y)/x²)/[1+(y/x)²]

(x+yy′)/(x²+y²)=(xy′-y)/(x²+y²)

x+yy′=xy′-y

(x-y)y′=x+y

y′=(x+y)/(x-y)

y′′=[(1+y′)(x-y)-(x+y)(1-y′)]/(x-y)²

将y′代入上式

y′′=[(1+(x+y)/(x-y))(x-y)-(x+y)(1-(x+y)/(x-y))]/(x-y)²

y′′=2(x²+y²)/(x-y)³

Answer 2

如图所示