Study

A study buddy for every subject.

Maths or history, biology or law: talk it through, work it out, and remember it on the day. Buddy helps you learn it, not just get it done.

  • Any subject, any exam
  • Hints before answers
  • Review cards from every session
courses.example.edu/hist210/week-5/1914
Screen shared Stop

Week 5: Why 1914 became a world war

Historians often group the long-term causes of the First World War as militarism, alliances, imperialism and nationalism.

In June 1914 the assassination of Archduke Franz Ferdinand in Sarajevo set off a crisis between Austria-Hungary and Serbia.

Within weeks, the alliance system drew in Russia, Germany, France and Britain, and a regional crisis became a continental war.

End
Listening

A history reading on your screen. Ask about it out loud, and Buddy answers about the page you’re on, in a sentence or two.

How it works

Learn it, don’t just finish it.

Whatever you’re studying, Buddy follows your page and helps only as much as you need, on iPad with your Pencil or on your Mac.

Press ⇧⌘Space from any app

Ask why, out loud.

Stuck on why something works? Ask. Buddy answers in a sentence or two, and you can cut in with your next question.

Ask about “this”.

A chapter, a case, a reading for class: scroll to the part that loses you and ask. Buddy answers about the page you’re on.

Write it by hand. Buddy checks it.

On iPad, ask “is this right?” and Buddy reads your handwriting, maths included, and circles the slip. Ask for the next step and it writes it under your line.

Library
All Notes18
My Notes14
Study Sessions4
Problems2
PDFs1
Review6
Folders
Algorithms7
Calculus5
Finance2
Organic Chemistry2
All Notes
Naming Organic Compounds11:02 AMFind the longest carbon chain… Note
The Chain Rule10:55 AMWhen one function sits inside… Note
Exam Plan — Week 610:29 AMChain rule practice set Note
Two Pointers12:56 AMOn a sorted array, walk one p… Note
Black–Scholes11:02 AMN(d2): the risk-neutral chance… Note
Binary Search11:02 AMdef lowerbound(nums, target): Note
Coin Change11:02 AMFewest coins that make up am… Note
Integration by Parts10:29 AMPick u with LIATE — the first o… Note
October 7, 2026 at 10:55 AM
NoteSessionsBrief

#The Chain Rule

When one function sits inside another, differentiate the outside, keep the inside, then multiply by the derivative of the inside.

ddxf(g(x))=f′(g(x))⋅g′(x)\frac{d}{dx}f(g(x)) = f'(g(x))\cdot g'(x)

Worked examples

ddxsin⁡(x2)=cos⁡(x2)⋅2x\frac{d}{dx}\sin(x^2) = \cos(x^2)\cdot 2x
ddx(3x+1)5=15(3x+1)4\frac{d}{dx}(3x+1)^5 = 15(3x+1)^4
Talk to Buddy⇧⌘Space
Review

Every session becomes review cards.

Each conversation is saved into your note with a summary and review questions. Practise them later with spaced repetition, or let Buddy quiz you out loud and grade your answers.

The Chain RuleWhat does the chain rule multiply by?
AnswerThe derivative of the inside function.
How it helps

It helps you learn. It won’t do it for you.

Buddy works the problem out quietly in the background, then gives you the smallest help that gets you moving again.

1

How do you want to work?

Talk it through together, or have a go on your own first.

2

A nudge

A question that points you the right way, from hints Buddy prepared in the background.

3

Point at the spot

The exact line on your page, or in your code.

4

Explain the idea

On a card or a diagram, not a lecture.

5

The full solution

Only when you ask for it.

FAQ

Questions, answered.

A friend to study with who’s always free. Pen Buddy’s Buddy sits in your notebook on Mac and iPad: you talk to it out loud, it follows the page you’re on, and it helps you work things out yourself, one small hint at a time.

Any subject. For subjects with problems to solve, like maths, physics, chemistry, economics and coding, Buddy helps you work them out one hint at a time. For reading subjects, like biology, history, law, medicine and languages, it explains the passage you’re on, draws timelines and diagrams, and quizzes you on what you read.

No, and that’s the point. You do the solving. Buddy gives the smallest help that gets you moving: a question, a hint, a pointer to the exact line, the idea on a card. A full solution comes only when you ask for one.

Yes. Highlight a passage in a PDF, or scroll to the part that loses you and ask about “this”, and Buddy explains it in a few plain sentences. On iPad it can draw a timeline or a diagram on your page, and every session leaves review questions for later.

Yes, on iPad. Write with Apple Pencil and ask “is this right?”. Buddy reads your handwriting, maths included, and circles the slip. Ask for the next step and it writes it by hand, under your line.

Yes. Every session is written into your note with a summary and review questions, and Buddy turns your notes into review cards with spaced repetition. It can also quiz you out loud and tell you how you did.

Work through problems with Buddy, then review what you did: each session leaves review questions in your notes, review cards come back when you’re about to forget them, and Buddy can quiz you out loud. It notices when you’ve been at it for a long time, and offers a break once.

On iPad, yes. Ask it to show you, and it draws timelines, flowcharts, trees and diagrams on your page. Write “graph: y = x² − 4” and Buddy plots it by hand, with the crossings marked.

Yes. On the Mac, Buddy is one shortcut away in any app and can follow your screen when you share it. On iPad, you get Pencil notes, Buddy’s handwriting and a study browser beside your page.

The whole notebook is free, with 25 credits a month to try Buddy. A credit is about one question. Regular $9.99 a month (300 credits), Heavy $24.99 a month (1,000 credits), Research $49.99 a month (2,500 credits).

Pen Buddy

Everything you need to study, and someone to study with.