Supose $p>1$ and $f,g\in L^p(\mathbb{R})$. Let $H(s)=\int_\mathbb{R}|f(x)+s\cdot g(x)|^p\mathrm{d}x$ for $s\in \mathbb{R}$. Show that $H$ is differentiable and find its derivative.
I've tried using the definition of derivative but haven't made any progress.