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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.

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    @t.b. You're right about the exponent, it's fixed now. Thanks for the hint!2012-01-12

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