Miss Kobayashi indulges in a little bit of relaxation in the eleventh episode of Miss Kobayashi’s Dragon Maid S, and then she learns a little more about Tohru’s past.

Tohru asks Elma and Takiya about Miss Kobayashi’s back pain
This episode of Miss Kobayashi’s Dragon Maid S begins with the adaptation of chapter 49, “Tohru & Relaxation”, from the sixth volume of the manga. The manga has a single panel showing Miss Kobayashi’s back pain, whilst the anime gives us a bit more. Just a relatively small scene of Miss Kobayashi throwing her back out whilst imitating an exercise from TV, though.
Tohru meeting with Elma and Takiya is the same, the conversation is more or less identical in both anime and manga.

Seems like Tohru’s tail can be more than just food
In both manga and anime, Tohru gives some serious thought to what it is that Miss Kobayashi actually wants. That leads us into the next part of the episode, which could be considered the main focus.

The Emperor of Demise
Once again from volume six, we get an adaptation of chapter 57, “Tohru & The Past (1)”. Before that, though, the anime adapts a minuscule part of chapter 56, “Tohru & Magic”, in which Miss Kobayashi notices the similarities between magic script and the programming language she uses at work.
Things get heavy as Tohru’s father tells Miss Kobayashi what happened before Tohru arrived in the human world.

Tohru’s first attempt at changing into human form is a success
After hearing what the Emperor of Demise has to say, Miss Kobayashi asks Tohru to hear more about her past. That leads into the adaptation of chapter 58, “Tohru & The Past (2)”, still from volume six.
Young Tohru’s outfit in her human form in the manga exposes a lot more skin than we see in the anime. Both anime and manga convey the same general idea, so there’s not much else to report on in terms of differences.
This was a particularly great, episode. I particularly enjoyed the glimpse into Tohru’s past, making her reasons for arriving in the human world clearer.
Next time is the final episode, so I’ll probably write a review for the season. Also, next episode is adapting one of my most wanted chapters, so we’re in for a treat.