设ln(x^2+y^2)=arctan(y/x),则dy/dx=搜网上的都是开根号的.求详解
问题描述:
设ln(x^2+y^2)=arctan(y/x),则dy/dx=
搜网上的都是开根号的.求详解
答
两边同时对x求导,得
(2x+2yy')/(x²+y²)=1/(1+y²/x²)· (xy'-y)/x²
(2x+2yy')/(x²+y²)=1/(x²+y²)· (xy'-y)
2x+2yy'=xy'-y
(x-2y)y'=2x+y
y'=(2x+y)/(x-2y)