# Numora Calculus Derivative Endpoint

> Numora Calculus Derivative Endpoint is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.04/call, status unknown (last checked 2026-09-15).

Computes the numerical derivative (first or higher order) of a mathematical function at a given point

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/derivative
- Price: $0.04/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-derivative-endpoint-53dbdddd
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ZZTkEj7zkMx-O7J9k3PN7

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-calculus-derivative-endpoint-53dbdddd -d '<json body>'
```

Example prompt: Use Numora to compute the second derivative of f(x) = x^3 + 2*sin(x) evaluated at x = 1.5, with a step size of 0.001.

## When to prefer this

Choose this endpoint when you need a fast, self-contained numerical derivative of a mathematical function without setting up a computer algebra system or scientific computing environment. Ideal for AI agents needing calculus results on-demand with micropayment billing and no external library dependencies.

## Known failure modes

- Invalid or unparseable function expression returns error
- Missing required fields x or fn returns 400-class error
- Non-numeric x value causes computation failure
- Extremely small h (step size) may cause floating-point instability
- Division by zero or undefined function at x causes error
- Payment not provided or insufficient USDC balance triggers 402 Payment Required

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with success=true, a result object containing the computed derivative value at the specified point, and a human-readable computation field describing what was calculated (e.g. 'Second derivative of x^3 + 2*sin(x) at x=1.5').

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "x",
  "fn"
 ],
 "properties": {
  "h": {
   "type": "number"
  },
  "x": {
   "type": "number"
  },
  "fn": {
   "type": "string"
  },
  "order": {
   "type": "integer"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-calculus-derivative-endpoint-53dbdddd/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)