This is actually for a Calculus question, but the Algebra part is what I'm stumped on.

I'm given the equation:

x^4 + y^4 + z^4 = 4xyz

And I will need to find the partial derivatives of z with respect to x and y. That part I can do. But I haven't been able to isolate z.

I feel like this should be relatively simple, but I'm missing something.