Chapter
What your import becomes, course included
The chapter is Orbily’s central brick. An import files your documents into the right folder and writes a structured, single-page course there: definitions, examples, formulas set apart, without you asking for any of it. Read it as is, have it rewritten from one instruction, and above all every AI tool uses it as its source.
Differentiation
···Differentiability at a point
What it means to have a tangent
A function can be continuous without being differentiable: continuity rules out jumps, differentiability rules out corners. It is the difference between drawing without lifting the pen and drawing without a kink.
The difference quotient
📖 Definition
f is differentiable at a if the difference quotient between a and a + h has a finite limit as h tends to 0. That limit is the derivative f′(a).
f′(a) = limh→0 f(a + h) − f(a)h
The slope of the secant tends to the slope of the tangent.
✏️ Example
x ↦ |x| is not differentiable at 0: the quotient is −1 on the left and +1 on the right. The two limits differ, so there is no tangent.
What you get
A one-page course generated on import, ready to read
Your original documents stay linked to the chapter
Rewrite, go deeper or fix errors with a single instruction
The single source behind flashcards, MCQs, sheets and cheat sheets
Good to know
A chapter holds a single-page course, meant to be read in one go. The Courses tool turns it into a lesson-by-lesson path with checkpoints, a final exam and progress tracking — from that same chapter if you want.
Your documents are saved either way. Open the chapter and start the generation yourself with the ✦ button.