 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ia/paper-2/10b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

\frac{\partial x _{i}}{\partial x _{j}} = δ_{ij},

where

δ_{ij}

is the Kronecker delta. Since

r = (x_{k} x_{k})^{1/2}

, the chain rule gives

\frac{\partial r}{\partial x _{j}} = \frac{x _{j}}{r} .

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