Plot3D[ArcTan[(x/y)],{x,-5,5},{y,-5,5}]

D[ArcTan[x,y],x]

D[ArcTan[x,y],y]

D[f[(x^2)-(y^2)],x]/x+D[f[(x^2)-(y^2)],y]/y

a=ContourPlot[x^2-y^2,{x,.1,1},{y,.1,1},WorkingPrecision->100]

b=VectorPlot[{1/x,1/y},{x,.1,1},{y,.1,1}]

Show[a,b]

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Plot3D[((x y)/(x^2+y^2)),{x,-5,5},{y,-5,5}]

Plot3D[(Sqrt[Abs[x y]]),{x,-5,5},{y,-5,5}]

Plot3D[((x (y^2))/((x^2)+(y^2))),{x,-5,5},{y,-5,5}]

Plot3D[Sign[(x^3)+(y^3)](((Abs[(x^3)+(y^3)]))^(1/3)),{x,-5,5},{y,-5,5},PlotPoints->1000]

Plot3D[((x^2)+(y^2)) Cos[(1/((x^2)+(y^2)))],{x,-.5,.5},{y,-.5,.5},PlotPoints->100]