Solving Partial Derivatives: x2+y2+z2=3xyz

[SelHype]

EDIT: I got it! I just used implicit differentiation to find it. Thanks for looking in here everyone!


x²+y²+z²=3xyz
Find the partial derivatives: z_x, z_y, and z_xy.


Okay so I know how to find the partial derivative, but I am not sure as to if I need to get the z on one side by itself. If that is what I need to do, then I am actually unsure as to how. I attempted to isolate z and ended up with z=$$\frac{x^{2}+y^{2}}{3xy-z}$$.

If I need to isolate z, then that is what I need help in doing. I know how to find the partial derivatives so I'm good there, but the z_x, etc., is just kind of confusing since he never went over anything like this in class and the book doesn't have it, either (it always has f_x).

EDIT: I got it! I just used implicit differentiation to find it. Thanks for looking in here everyone!

 

[kurt.physics]

The partial derivatives are as follows: z_x=\frac{2x}{3xy-z} z_y=\frac{2y}{3xy-z} z_{xy}=\frac{2}{3xy-z}