ln(x^2+y^2)=arctan(y/x) 求导

题目

ln(x^2+y^2)=arctan(y/x) 求导
隐函数求导

答案

方程两边对x求导
(2x+2yy')/(x^2+y^2)=[(xy'-y)/x^2]/[1+(y/x)^2]
2(x+yy')/(x^2+y^2)=(xy'-y)/(x^2+y^2)
2x+2yy'=xy'-y
(x-2y)y'=2x+y
y'=(2x+y)/(x-2y)