 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/11/a/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

y

gives

(\frac{\partial f}{\partial x})_{y} = (\frac{\partial f}{\partial u})_{v} (\frac{\partial u}{\partial x})_{y} + (\frac{\partial f}{\partial v})_{u} (\frac{\partial v}{\partial x})_{y} .

The held-fixed variables distinguish the two coordinate descriptions; the same scalar function is being differentiated.

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