How to Calculate Force and Work from a Potential Function in Physics?

[imy786]

Homework Statement

A particle moving in the x - y plane is subject to a conservative force F(x, y)
whose potential function is V = Kx^3y^ 2, where K is a constant.
Evaluate F(x, y). Also, determine the work done on the particle by this force
in moving it from the origin, x = O, y= O, to the point x = 2, y= 4.


2. Homework Equations

$$\vec{f}=-\vec{\nabla}\,U\Rightarrow \vec{f}=-\left(\frac{\partial U}{\partial x},\frac{\partial U}{\partial y},\frac{\partial U}{\partial z}\right)$$

The Attempt at a Solution

$$U(x) = \frac k (x^3) y^2$$

work done= force*distance

force:

$$\vec{f}=-\vec{\nabla}\,U$$

 

[malawi_glenn]

it is straightforward to derive the force from that potential, can you do it? or have you tried?