Hi!

I Can't seem to find the critical points of the function f(x,y) = x*y*ln(x^2 + y^2)

I did the df/dx = y*[ (2 x^2)/(x^2 + y^2) + ln(x^2 + y^2) ]

and the df/dy = x*[ (2 y^2)/(x^2 + y^2) + ln(x^2 + y^2) ]

I equalled them both to 0, but now I'm stuck because I don't know how to solve the system:

y*[ (2 x^2)/(x^2 + y^2) + ln(x^2 + y^2) ] = 0

x*[ (2 y^2)/(x^2 + y^2) + ln(x^2 + y^2) ] = 0

I have the solutions. There are 4 critical points and none of them is x=0 or y=0.

But I don't know how to get to the solution.

Thanks in advance!

Tony