求隐函数arctan(y/x)=ln√x²+y²的导数dy/dx．

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