I'm trying to solve that this function is convex, but, I'm still stuck with it.
If there is a function $f(x,y) = x^xy^y$, where $x,y > 0$, how could I prove that this function is convex?
My thought : I think that it is impossible to use the definition directly. Instead, even though we can use the hessian matrix (i,e, if I prove its hessian matrix is positive definite or positive semidefinite, we are done), I'm still don't know.