  We study connections between the $W^1_p$-differentiability and the
$L_p$-differentiability of Sobolev functions. We prove that,
$W^1_p$-differentiability implies the $L_p$-differentiability, but the opposite
implication is not valid. The notion of approximate differentiability is
discussed as well. In addition, we consider the $W^1_p$-differentiability of
Sobolev functions $\cp_p$-almost everywhere.

Analysis of PDEs