PowerItAppearsTo​(AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

Once the expression is read through its logarithm, ln(expr) holds
ln(target) multiplied by exactly this power -- so it is the coefficient the
dropped 1/(12f) arrives with, and the same guard as everywhere else applies
to it. Only multiplication, division and a constant power keep a factor a factor; a
sum does not (x! + x is not a fixed power of the factorial at all), and
neither does an exponent that moves -- for (x!)^x the power is x,
x/(12x) does not vanish, and it is refused.
Read off the shape rather than by differentiating and simplifying. That is the same
answer at a fraction of the cost: the symbolic route needs a full
Simplify(System.Int32) to cancel the target back out -- InnerSimplified leaves p * (1/x^x) / (p/x^x) standing -- and it is asked on every expression
holding a factorial.