I mean, the notation $x^{\alpha} = x_1^{\alpha_1}x_2^{\alpha_2}...x_n^{\alpha_n}$ for $\alpha = (\alpha_1,..., \alpha_n)$ and $|x|$ is the sum of all (?) So I don't see how that would be possible (if it is...) How should one so choose $\alpha$? A brief explanation would be really appreciated.
I understand however that for distributions, $$\partial ^\alpha f= \partial_1^{\alpha_1}\cdots \partial_n^{\alpha_n}f$$ and if all $\alpha_i = 0$ then no differentiation is made.
So what applies here?