helpppppppp physics question

Question

A potential energy function for a two-dimensional force is of the form U = 3 x5y - 3 x. Find the force that acts at the point (x, y). (Use x and y as appropriate.)

 

__________i+___________j

Answer 1

Porcia,

 

Do you mean 

 

U(x,y) = 3x⁵y - 3x ?

 

If so, then

 

F_x = -∂U/∂x = -15x⁴y + 3

F_y = -∂U/∂y = -3x⁵

 

F = (-15x⁴y + 3)i + (-3x⁵)j