ln√(x^2+y^2)=arctan(y/x)的导数dy/dx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/22 21:33:18
ln√(x^2+y^2)=arctan(y/x)的导数dy/dxln√(x^2+y^2)=arctan(y/x)的导数dy/dxln√(x^2+y^2)=arctan(y/x)的导数dy/dx即0.5

ln√(x^2+y^2)=arctan(y/x)的导数dy/dx
ln√(x^2+y^2)=arctan(y/x)的导数dy/dx

ln√(x^2+y^2)=arctan(y/x)的导数dy/dx
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)'

(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)

(2x-y)*y'=x+2y
所以
dy/dx=(x+2y)/(2x-y)