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

Question 92

Essay

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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