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A potential energy function for a two-di...

A potential energy function for a two-dimensional force is the form `U=3x^2y-7x`. Find the force that acts at the point `(x,y)`.

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`F_x=-(delU)/(delx)=-(del(3x^3y-7x))/(delx)=-(9x^2y-7)=7-9x^2y`
`F_y=-(delU)/(dely)=-(del(3x^3y-7x))/(dely)=-(3x^3-0)=-3x^3`
Thus, the force acting at point `(x, y)` is
`vecF=F_xhati+F_yhatj=(7-9x^2y)hati-3x^3hatj`
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