ableitungen-quiz

Five chain- and product-rule exercises that check the answer you type, not a multiple choice. One index.html, no build step, no backend.

Why

Derivatives are learned by writing them, and "is 15(3x+2)^4 the same as 5(3x+2)^4·3?" is exactly the question a tutor answers twenty times. The page types the answer, evaluates it, and says what went wrong: still f(x) itself, a known mistake (missing inner derivative, missing factor ½, one product-rule term dropped), or the first x where the typed term and the correct one disagree, with both values.

The second constraint was the device: it has to be readable on an iPad from QuickLook or an Element preview, where no JavaScript runs. So the page carries a <details> copy of all five tasks with hints and solutions, and the no-JS view is what you see there.

Run

Open index.html in a browser — file:// is enough:

xdg-open index.html

Math is typeset by MathJax 3 from a CDN; offline the formulas show as raw \( … \). State (index, tries, hints used, solutions seen) is kept in localStorage under kgpr-v1, so a reload continues where you stopped. "Nochmal von vorn" resets it.

How an answer is checked

The page contains a small expression parser, not a CAS:

1. Normalise — drop a leading f(x) = / f'(x) =, map − – — to -, · × ⋅ to *, ÷ to /, ²/³ to ^2/^3, √ to sqrt, , to ., lowercase.
2. Tokenise / parse — recursive descent over + - * / ^, parentheses, implicit multiplication (2x, 3(x+1), x sin(x)), right-associative ^, unary minus, functions sin cos tan ln log exp sqrt, constants pi, e, and sin x without brackets. Unknown characters and unterminated terms throw a readable error.
3. Compare numerically — both terms are evaluated at nine fixed points (-1.7, -0.83, 0.31, 0.77, 1.13, 1.69, 2.41, 3.07, 3.71) and accepted if they agree within 1e-7 · (1 + |a| + |b|) on at least three finite points.

Wrong answers are then diagnosed in order: equal to f(x) → "that is still the function"; equal to one of the 21 curated wrong answers → its specific explanation; otherwise the first differing point is printed with both values.

Tests

node check.mjs     # 51 assertions, exit 0 = all pass

Node 18+ (ESM, top-level await), no dependencies. The script cuts the <script> block between const TASKS and /* ---------- Zustand out of index.html and evaluates it, so the test runs the same parser and task data the page runs — no copy to drift. Renaming either marker makes it fail with "Marker in index.html nicht gefunden".

What the 51 assertions cover:

• 5 — each task's stored answer matches the central difference (f(x+h)-f(x-h))/2h of its own f (h = 1e-6, rel < 1e-4).
• 5 — f(x) itself is not accepted as its derivative (the "not derived yet" hint).
• 21 — every wrong answer listed for a task is genuinely wrong.
• 10 — parser edge cases: implicit multiplication, f'(x)= prefix, √, -x^2, 2^3^2 = 512, sign errors detected, e as Euler's number, sin x.
• 4 — malformed terms (x+, sin, 2*, (x+1) throw instead of silently evaluating to nonsense.
• 6 — the no-JS copy lists 5 tasks and each data-answer equals the task's answer.

Measurements

$ node check.mjs | tail -3
ok   statische Aufgabe 5 trägt dieselbe Antwort wie TASKS

alle Prüfungen bestanden
$ node check.mjs | grep -c '^ok' ; node check.mjs | grep -c '^FAIL'
51
0

Worst relative deviation between a stored answer and the numeric derivative, across the five tasks: 7.6e-11 (the check allows 1e-4). index.html is 25 KB.

Deviations

• Numeric equivalence, not symbolic. Two terms that agree on the nine sample points count as equal — a term that is wrong only between them (or zero at all nine) passes. Sampling nine points is the price for not shipping a CAS.
• The no-JS copy duplicates the task text. It has to: it is what iPad QuickLook shows. check.mjs keeps the answers in sync; the prose is maintained by hand.
• German only, and the feedback text assumes a student reading German.
• MathJax from a CDN. No vendored copy, so the page needs network for typeset math; the quiz itself works without it (raw LaTeX instead of formulas).
• Revealing a solution counts as done. The summary distinguishes "selbst gelöst" from "Lösung angesehen", but both advance.
• Answers must be typed in the notation the parser knows; \frac, log_2, absolute values and |x| are not supported.