I don't really understand this calc question What do you even do here? Take the other two variable to RHS?


HINT:
Start by considering, 
$$z^z = \dfrac{c}{x^xy^y}$$
Next, apply logarithm laws to obtain, 
$$z\log (z) = \log (c) - x\log (x) + y\log (y)$$
Hopefully, from here you can apply ideas of partial differentiation to obtain your answer (the product rule will come in handy). 
