Question 944577
Let {{{u=x^2+y^2}}},
{{{d(y/u)/dx=-(y/u^2)(du/dx)=-(y/u^2)(2x)=(-2xy)/(x^2+y^2)^2}}}
Similarly, 
{{{d(-x/u)/dy=-(-x/u^2)(du/dy)=(x/u^2)(2y)=(2xy)/(x^2+y^2)^2}}}
Adding them together,
{{{d(y/(x^2 + y^2))/dx + d((-x)/(x^2 + y^2))/dy=0}}}