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fixed point _convergence _check


In fixed point methodes to find out 
convergence we need to check 

[nonlinear system...
  u(x,y)=x^2+xy-10  = 0
  v(x,y)=y+3xy^2-57 = 0
]

&#948;u/&#948;x+&#948;V/&#948;x < 1          &#948;<-means partial
derivative
and
&#948;u/&#948;y+&#948;V/&#948;y < 1

means, after find out jacobian ,mathematica
will inserts x,y value into
&#948;u/&#948;x,&#948;V/&#948;x,&#948;u/&#948;y,&#948;V/&#948;y
and show me &#948;u/&#948;x+&#948;V/&#948;x =?
,&#948;u/&#948;y+&#948;V/&#948;y=?
how i can do that with mathematica ?

Please help me .


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