  One of the classical results concerning differentiability of continuous
functions states that the set $\mathcal{SD}$ of somewhere differentiable
functions (i.e., functions which are differentiable at some point) is Haar-null
in the space $C[0,1]$. By a recent result of Banakh et al., a set is Haar-null
provided that there is a Borel hull $B\supseteq A$ and a continuous map
$f\colon \{0,1\}^\mathbb{N}\to C[0,1]$ such that $f^{-1}[B+h]$ is Lebesgue's
null for all $h\in C[0,1]$.
  We prove that $\mathcal{SD}$ is not Haar-countable (i.e., does not satisfy
the above property with "Lebesgue's null" replaced by "countable", or,
equivalently, for each copy $C$ of $\{0,1\}^\mathbb{N}$ there is an $h\in
C[0,1]$ such that $\mathcal{SD}\cap (C+h)$ is uncountable.
  Moreover, we use the above notions in further studies of differentiability of
continuous functions. Namely, we consider functions differentiable on a set of
positive Lebesgue's measure and functions differentiable almost everywhere with
respect to Lebesgue's measure. Furthermore, we study multidimensional case,
i.e., differentiability of continuous functions defined on $[0,1]^k$. Finally,
we pose an open question concerning Takagi's function.
