原式化简为1/2ln(x^2+y^2)=arctany/x
两边对x求导,得
1/2×1/(x^2+y^2)×(2x+2yy')=1/[1+(y/x)^2]×(y'x-y)/x^2
化简得
y'=(x+y)/(x-y)
则dy/dx=(x+y)/(x-y).
很高兴为你解答,希望对你有所帮助,