Formula Derivation Tree (Family Map)
A tree showing how formulas grow from a few root formulas.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Paste the prompt into the chat.
- 2. Enter chapter, class, and board.
- 3. Send and study the tree structure.
- 4. Ask to expand any branch further.
- 5. Copy into a document or redraw on board.
🔧 If it is not right, reply with this: If a branch link is wrong, reply: "The link from [root] to [formula] is not valid. Correct the derivation chain and verify each step."
THE PROMPT
ROLE: Act as a mathematics teacher who shows students how formulas descend from a few roots.
CONTEXT: I teach [CLASS/GRADE] for the [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. Students think every formula in [CHAPTER NAME] is separate and must be memorised. I want a DERIVATION TREE showing how most formulas grow from a small set of root formulas, so they have far less to memorise.
YOUR TASK:
1. Identify the few ROOT formulas of the chapter that everything else comes from.
2. Build a text-based tree (indented branches) showing which formulas derive from which root, level by level.
3. On each branch, write a 3-to-6 word note on the step that gets you from parent to child.
4. Mark clearly which root formulas truly must be memorised.
INPUT: Here is the chapter and class. Chapter: [PASTE HERE]. Class/Board: [PASTE HERE].
HOW TO WORK IT OUT: Internally trace each derivation chain from root to leaf and confirm each link is a valid step. VERIFY two ways: (a) check that each child formula really can be derived from its stated parent; (b) confirm the root set is genuinely sufficient to reach all the leaves. Never invent a false derivation link or formula. Keep all maths fully legible in clean plain text or simple LaTeX, and use simple indentation so the tree reads clearly as plain text.
OUTPUT FORMAT (use this exact order):
1. TITLE: '[Chapter] - Formula Derivation Tree (Class [X], [Board])'.
2. 'Compiled by [YOUR NAME]'.
3. 'Memorise only these roots:' a short list of root formulas.
4. The indented tree, with a tiny step-note on each branch.
5. A closing line: 'Total to memorise: [N] roots instead of [M] formulas.'
6. Footer line.
RULES: Every branch link must be a valid derivation. Roots must truly be sufficient. Accurate formulas only.
MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.
GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.
SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
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