  For the Minkowski question mark function $?(x)$ we consider derivative of the
function $f_n(x) = \underbrace{?(?(...?}_\text{n times}(x)))$. Apart from
obvious cases (rational numbers for example) it is non-trivial to find explicit
examples of numbers $x$ for which $f'_n(x)=0$. In this paper we present a set
of irrational numbers, such that for every element $x_0$ of this set and for
any $n\in\mathbb{Z}_+$ one has $f'_n(x_0)=0$.
