Question

A potential energy function for a two-dimensional force is of the form U = 3x3y – 7x. Find the force that acts at the point (x, y).

Answer 1

The x force is -dU/dx (partial derivative)
The y force is -dU/dy (partial derivative)

You should place a ^ before exponents, as in
U = 3x^3* y -7x

I assume you know how to take partial derivatives. Treat the other variables as constants.

Answer 2

9x^2y-7,3x^3

Answer 3

Since F = -(dU/dx)i -(dU/dx)j

-(dU/dx) = - (9x^2y - 7)i
-(dU/dy) = - (3x^3)

F = -(dU/dx)i -(dU/dy)j = (-9x^2y+7)i - 3x^3j

Answer 4

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