The calculation of Gateaux derivative

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How to calculate the Gateaux derivative of the following functional especially when $p$ is not a integer where $\Omega \subset \mathbb{R}^n$ is an open set ?

$I(u)=\int_{\Omega} |u|^p dx$

Besides, how to prove that $I(u)$ is Frechet differentiable?

Thanks for any help!