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I have a function $f(x) = (\mathbf x ^ \top \mathbf x) ^ {p/2}$.

Its gradient is $\nabla f(x) = 2p (\mathbf x ^ \top \mathbf x) ^ {(p-2)/2} \mathbf x$

How do I compute its Hessian $\nabla^2f(x) $? Should I use product rule? Can someone show me how to do it or refer me to some resource?

Thanks

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    The factor 2 in the gradient should not be there!2012-02-12
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    Note also that $\nabla^2$ is conventionally used to denote the Laplacian $\Delta$. In a way $\Delta = \nabla \cdot \nabla$ whereas the Hessian is given by the dyadic product $\nabla \otimes \nabla$.2012-02-12

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