I want to find $u''$ in the distributional sense, where $u(x) = (1+|x|)^{-2}$ But I am very confused on how to do it.
I think this is right: $\langle u'', \varphi \rangle = \langle u',\varphi ' \rangle = \langle u, \varphi ''\rangle = \int_{-\infty}^{\infty} (1+|x|)^2 \varphi''(x)\ dx $ But I am very lost on how to continue from here.
Any help would be appreciated.