# Numora Calculus Derivative Endpoint

> Numora Calculus Derivative Endpoint is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

Numerically computes the derivative of a mathematical function at a specified point, supporting higher-order derivatives.

## Facts

- Endpoint: POST https://numormo.vercel.app/api/calculus/derivative
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-derivative-endpoint-9184d183
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_FmauKtX1tzOQyaAk0-tEb

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-9184d183 -d '<json body>'
```

Example prompt: Can you compute the second-order derivative of f(x) = x^3 - 2*x + 1 at x = 2 using a step size of 0.001?

## When to prefer this

Choose this endpoint when you need a fast, self-contained numerical derivative without setting up a symbolic math library or CAS (computer algebra system). Ideal for AI agents doing optimization, physics simulations, or engineering calculations where approximate numerical differentiation is sufficient. Prefer over symbolic solvers when the function is given as a string expression and exact symbolic output is not required.

## Known failure modes

- Invalid or unparseable function expression returns an error
- Division by zero or singularity at the evaluation point may produce NaN or Inf
- Missing required fields 'x' or 'fn' results in a 400-level error
- Extremely small or zero step size h may cause numerical instability
- Very high derivative order may accumulate floating-point errors
- Payment failure via x402 prevents endpoint access

## 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 a boolean 'success' field, a 'result' object containing the computed derivative value at the given point, and a 'computation' string that describes in human-readable form what was calculated (e.g. 'Second derivative of x^3 at x=2').

## 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-9184d183/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)