Question

ln√(x^2+y^2)=arctan(y/x)的导数dy/dx

Answer 1

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)