Calculus

Derivatives and integrals per rule — the integrals exist because they were built backwards.

equations.calculus · v1 · renderer math

1. d/dx [ -5x^2 + 2x - 2 ] → -10x + 2 2. d/dx [ -6exp(x^2) ] → -12x*exp(x^2) 3. d/dx [ -5sin(4x) ] → -20cos(4x) 4. d/dx [ (2x + 2)sin(x) ] → 2sin(x) + (2x + 2)cos(x) 5. d/dx [ -6sin(x) + 4x ] → -6cos(x) + 4 6. d/dx [ 4exp(-3x) ] → -12exp(-3x)

Controls · from schema()

Mode

Rule

How many

1 40

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from ISS Position.

seed token 3JRNZ4SXP8FK9N6Y1EEPKDGX54

Re-render keeps this token. Generate replaces it. That is the whole idea.

Printable worksheet 20 problems · answers on page 2

The seed is printed in the footer, so the same sheet comes back from the same link — and a different seed is a different sheet.

entropy in

16 bytes

stream used

39 bytes

rejections

duration

1,301 µs

problems

Seed receipt

Class C · Observational

The ISS was over 21.05° N, 3.64° E — 1,770 km north of Accra — when this was drawn.

Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.

source: ISS Position
observed: 2026-10-28T22:13:11+00:00
latency: 157ms
mixed with: csprng — always

https://www.openstreetmap.org/#map=3/21.05/3.64 ↗

Permalink

The token is the seed, so this link recomputes the result rather than looking it up. No database, and it works for as long as v1 does.

This page and /api/v1/g/equations.calculus run the same code. There is no private endpoint.

Calculus

Result

Measurements

Seed receipt

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