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InnerDifferentiate(AngouriMath.Entity.Variable)

Method (no overloads)

Summary

(x!)' = Γ(x + 1) ψ(x + 1), which needs a symbolic gamma and polygamma the
library does not have — so this declines rather than answering.

Remarks

It used to answer NaN, which says the derivative does
not exist. It does: x! is Γ(x + 1) and the library already
evaluates it away from the integers — (1/2)! is 0.886… — so it is
smooth except at the poles, and d/dx x! at 3 is an ordinary
Γ'(4) ≈ 3.966. Saying NaN was a wrong answer rather than a missing
feature, and it propagated: one factorial anywhere turned an otherwise fine
derivative into NaN.
https://github.com/asc-community/AngouriMath/issues/958
Returning the unevaluated derivative is what every other node the library cannot
differentiate already does — apply(f, x) among them — and it is what
AGENTS.md asks for: unevaluated means "I could not settle this", NaN means "this does not exist", and only the first is true here.
Computing it properly is
#171, which is
a separate and larger piece of work; this rule stays correct once that lands.

AngouriMath

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AngouriMath

InnerDifferentiate​(AngouriMath.​Entity.​Variable)

InnerDifferentiate(AngouriMath.Entity.Variable)