Question: Determine whether or not the vector function is the gradient f(x,y)f(x,y) of a function everywhere defined. If so, find all the functions with that gradient.(x3+y)i+(7y3+x)j(x3+y)i+(7y3+x)j

Determine whether or not the vector function is the gradient f(x,y)f(x,y) of a function everywhere defined. If so, find all the functions with that gradient.(x3+y)i+(7y3+x)j(x3+y)i+(7y3+x)j Not a gradient x3y+y22+Cx3y+y22+C x44+xy+7y44+Cx44+xy+7y44+C x3+y+Cx3+y+C 7y3x+x22+C7y3x+x22+C None of these.

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