 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/5/solution

Take the Cartesian partial derivatives component by component. The divergence is

\nabla \cdot F = - e^{- x} cos z - e^{- y} sin z .

The constant third component has zero derivatives. The curl consequently has only two nonzero components:

\nabla \times F = (- e^{- y} cos z, - e^{- x} sin z, 0) .

 New to topics? Read the docs here!