Help understanding vector-by-vector differentiation identity

Question

So I have very recently been introduced to matrix caluclus, and I have read and been following the quite nice Wikipedia article on the topic (link). However, I do have a bit of trouble understanding this vector by vector identity.
$$\frac{\partial \boldsymbol{x}}{\partial \boldsymbol{x}}=\boldsymbol{I}$$ where $\boldsymbol{I}$ is the identity matrix.
So, here is my question where does this identity come from and how is it derived? From my point of view I don't get why a vector suddenly can become a matrix. Any help on how to derive this identity will be highly appreciated.