How would I write the product of something whilst also omitting an element?

Question

I have a function $$f(x_1,x_2,...,x_n) = \prod_{i=1}^{n}x_i^{\alpha_{i}}$$

I want to take the partial derivative $$\frac{\partial f}{\partial x_k}$$

Now I believe this will look like $${\alpha_kx^{\alpha_k-1}} \cdot \prod_{i=1}^{n} x_i^{\alpha_i} $$

This isn't actually correct. The last product will be omitting the $k^{th}$ term. But I am not sure how to write that out?

Answer 1

The standard notation is to use a hat: writing, for instance, $(a_1,...\widehat{a}_i, …, a_n)$ means that you do not consider the $i$-th term. In this case, however, simply writing: $$ \prod_{1 \leq i \leq n, \, \, i \neq k} x_i ^{\alpha_i} $$ works as well.