求隐函数arctan(y/x)=ln√x2+y2的导数dy/dx．
两边关于x求导，得 1/[1+(y/x)2]•(y/x)′x=1/2•[1/(x2+y2)•(x2+y2)′x x2/(x2+y2)•(y′x-y)/x2=1/2•(2x+2yy′)[(y′x-y)/(x2+y2)]=(x+yy′)/(x2+y2) 所以y'(x-y)=x+y
求隐函数arctan(y/x)=ln√x2+y2的导数dy/dx．
两边关于x求导，得 1/[1+(y/x)2]•(y/x)′x=1/2•[1/(x2+y2)•(x2+y2)′x x2/(x2+y2)•(y′x-y)/x2=1/2•(2x+2yy′)[(y′x-y)/(x2+y2)]=(x+yy′)/(x2+y2) 所以y'(x-y)=x+y
