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derivative of (N + x) \log \frac{N + x}{(N + 2x) p} + x \log \frac{x}{(N + 2x)(1 - p)} in x
derivative of (N + x) \log \frac{N + x}{(N + 2x) p} + x \log \frac{x}{(N + 2x)(1 - p)} in x
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