Proof of a result in $W^{1,p}$

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I have to do this exercise:

$\bullet$ Given $u \in W^{1,p}$ and $h=te_i$, $1\leq i\leq N$, prove that $D_hu$ converges to the $i$-th weak partial derivative of $u$, as $t\rightarrow 0$ in $L^p(\omega)$, $\omega \subset \subset \Omega$.

I have no idea how to solve it, can anybody help me? Even a hint would be useful. Thanks