If $x^x y^y z^z = c$, then the value of $\frac{\partial^2z}{\partial x \partial y}$ at $x = y = z$ is?
I found a similar question on this site (If $x^y y^x z^z=c$, then find $\frac {\partial^2z}{\partial x \,\partial y}$ at $x=y=z$.). But the problem is, when I solve for Z , and take log both sides I get this $zln(z) = ln(c) - xln(x) - yln(y)$ Now if I partially differentiate it w.r.t. x, then y term vanishes (constant when differentiating w.r.t. x), and now again I partially differentiate w.r.t. y, then I get 0. Please help me to solve this question.