 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/11/a/ii/solution

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

a \neq = 0

and

∣ x / a ∣ < 1

. Its logarithmic expression gives

y = \frac{1}{2} lo g \frac{1 + x / a}{1 - x / a}, y^{'} = \frac{a}{a ^{2} - x ^{2}} .

The same derivative holds on a differentiable complex branch away from its singularities.

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