ln√(x^2+y^2)=arctan(y/x)的导数dy/dx
问题描述：
ln√(x^2+y^2)=arctan(y/x)的导数dy/dx
答
即0.5ln(x^2+y^2)=arctan(y/x)对x求导得到0.5(2x+2y*y')/(x^2+y^2)= 1/(1+y^2/x^2) *(y/x)'即(2x+2y*y')/(x^2+y^2)=2x^2/(x^2+y^2) *(x *y'-y)/x^2于是x+y*y'=2(x *y'-y)即(2x-y)*y'=x+2y所以dy/dx=(x+2y)/(2x-y)...