Expressed all partial derivatives

[Yegor]

I'm given F(x*y;z/x), where z=z(x,y).
I have to proof that (∂z/∂x)*x+(∂z/∂y)*y=3*z
I have expressed all partial derivatives, but I got only (∂z/∂x)*x-(∂z/∂y)*y=z
I think that it's impossible at all to solve this problem, because z is arbitrary function as i understand.
Help me please. Where I'm wrong?

 

[Yegor]

I made it. And received (∂z/∂x)*x-(∂z/∂y)*y=z
Did anyone get (∂z/∂x)*x+(∂z/∂y)*y=3*z ??
I've denoted already many hours for this problem and many times got "incorrect" answer. Now I think that my solution is correct and something is wrong with a "handwritten answers" on the sheet with problems

 

[OlderDan]

I'm given F(x*y;z/x), where z=z(x,y).
I have to proof that (∂z/∂x)*x+(∂z/∂y)*y=3*z
I have expressed all partial derivatives, but I got only (∂z/∂x)*x-(∂z/∂y)*y=z
I think that it's impossible at all to solve this problem, because z is arbitrary function as i understand.
Help me please. Where I'm wrong?

Have you stated the problem correctly?

Consider the variables u = x*y and v = z/x and take the partial derivatives of F using the chain rule