 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-2/10/solution

Differentiate the three components with respect to their matching Cartesian coordinates:

\nabla \cdot F = y^{2} z^{2} + 4 y^{3} + x^{3} y^{2} .

The

3 x z^{2}

term contributes nothing to the

y

derivative because it is independent of

y

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