Summer of Math Exposition

Overall: 4,75/9 - First of all, I felt no motivation to watch this video. Showcasing some cool connections between derivative and other stuff (like where can we use it etc.) would definitely help. I know that this video was meant for students that are trying to learn what derivatives are, but a bit of motivation wouldn’t hurt anyone. The explanation was good, but I felt like the beginning was rushed -> I would focus more on the intuition behind derivative (maybe by showcasing it in different forms?) and take a few minutes from explaining what the product rule and chain rule are. I liked that you collected different approaches to derivatives, it was refreshing. Also, the design… yeah, it was basic and it did it’s job, but nothing more. It’s not quite memorable, because nothing was novel here. Neither graphic or didactic approach to deivatives. Nonetheless I think it’s a great start to making a yt math explainers channel :D

Congratulations on your first video! This is quite pleasant to watch and well-paced, but I do find the level expected from the viewer too in-homogeneous to be helpful in understanding the concepts introduced. Indeed, you cover three topics of largely different levels (spanning high-school to grad studies), and while each section introduces interesting ideas, I found you did not take the time to really explain these concepts before moving on to the next one. I believe this video would gain from being split into three sub-videos, each corresponding to the three levels you explained.

Overall pleasant and with interesting key points, but a bit too scattered to be used in its exact form.

You indicated high-school students as part of the target audience, but the language you use is too technical and beyond their reach, I could never propose such content to them. Assuming instead that it is intended for university students, the video is not very different from a standard lecture. It risks becoming boring; personally, I would prefer studying from a book (which would also make note-taking easier). When I studied Lie structures on manifolds in books, I found interesting ideas and suggestions that are missing here. Suggestion: try to find something original, think of students who struggle the most, and avoid putting all this material into a single video. Instead, create several shorter videos, divided by topic and level of difficulty.

I like all the alternative definitions, and you do a good job illustrating the standard one. I would suggest labeling the points and line segments for colorblind accessibility. The other approaches all need motivation (and ideally visualization). Why should we expect the commutator or the linear algebra to be relevant?

Too much material