If $x^y y^x z^z=c$, then find $\frac {\partial^2z}{\partial x \,\partial y}$ at $x=y=z$. If $x^y y^x z^z=c$, then find $\dfrac {\partial^2z}{\partial x \,\partial y}$ at $x=y=z$.
I tried taking $\log$ but that doesn't help.
Any hints will be appreciated. Thanks.
This is what I have tried:



Here is the solution:
Hopefully the image is clear and helpful

