hook_taxonomy_term_update(), where does it get invoked in drupal's core code? I looked after a module_invoke_all('taxonomy_term_update') in the taxonomy module (and more in the entire Drupal core) but I didn't find anything. 

Where does that hook get invoked in the code?
It's invoked from taxonomy_term_save().

The reason you can't find it is because the hook gets invoked via an interpolated string, depending on the current operation (insert or update):

module_invoke_all("taxonomy_term_$op", $term);