Taylor series of upx function

[Kouznetsov]

Is it possible to find an expression of, say \( (\text{sexp}_e x)' \) in 0?

Why I ask it? Because there is a property:
\( \ln f'(x)=f(-1)+f(0)+...+f(x-1) + \ln f'(-1) \)

Dear Ansus. Do you mean that \( f \)=sexp ?
I cannot understand the equation you wrote.
The similar equation I can deduce is
\( \ln(f'(x))=f(-1)-f(0)+f(x-1) + \ln(f'(x-1)) \),
but I do not see, how does it help to get a simple expression for \( f'(0) \).