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Find a Function Of f(x,y)f ( x , y ) Such That

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Find a function of f(x,y)f ( x , y ) such that f=F(x,y)=(y1+x2y2,x1+x2y2)\nabla f = \mathrm { F } ( x , y ) = \left( \frac { y } { 1 + x ^ { 2 } y ^ { 2 } } , \frac { x } { 1 + x ^ { 2 } y ^ { 2 } } \right) .

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Definitions:

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A reinforcement schedule in which rewards are provided after an unpredictable time interval, leading to reasonably steady response rates.

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In psychology, to diminish a conditioned response by repeatedly presenting the conditioned stimulus without the unconditioned stimulus.

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A behavioral psychology principle where the removal of an unfavorable outcome or stimulus strengthens a behavior or increases its likelihood of recurrence.

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