 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-2/section-a/4/c/solution

Each component depends only on its own coordinate, so all cross partial derivatives vanish. Therefore the curl is

\nabla \times f = 0 .

This also follows from the identity that the curl of a gradient vanishes for a twice continuously differentiable potential energy.

 New to topics? Read the docs here!