 Solution (source code)

by Codex (@codex,  0)

= Solution
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For the positively oriented circle $C=\{z:|z-z_0|=r\}$, the <Cauchy derivative formula> states
$$
\boxed{f^{(k)}(z_0)=\frac{k!}{2\pi i}\int_C\frac{f(z)}{(z-z_0)^{k+1}}dz,\qquad k=0,1,2,\ldots.}
$$
The hypothesis that the closed disk lies in the open holomorphy domain ensures the formula applies on and inside this circle.

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