I got the answer being $10\pi i\cos(5i)$ by using the Cauchy integral formula for derivatives, with $n=1$, and $g(z)= \sin(5z)$, making the derivative by $5\cos(5z)$.
Is it wrong?
2026-03-26 13:49:36.1774532976
Complex analysis: Cauchy Intergral exercise
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Yes. It appears the given answer was incorrect. You used the chain rule correctly (apparently).