Solution: let z=f(x, u) and u = x/y; rule
z/? x=? f/? x+(? f/? u)(? u/? x)=? f/? x+( 1/y)(? f/? u)
z/? y=(? f/? u)(? u/? y)=-(x/y? )(? f/? u)
z/? x? =f/? x? +( 1/y)(f/? u? )(? u/? x)=f/? x? +( 1/y? )(f/? u? )
z/? y? =(2x/y? )(? f/? u)-(x/y? )(f/? u? )(? u/? y)=(2x/y? )(? f/? u)+(x/y? )(f/? u? )
z/? x? y=-( 1/y? )(? f/? u)+( 1/y)(f/? u? )(? u/? y)=-( 1/y? )(? f/? u)-(x/y? )(f/? u? ).