# Numora Calculus Derivative API

> Numora Calculus Derivative API is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-13).

Computes the numerical derivative of a mathematical function at a specified point, with support for higher-order derivatives and configurable step size.

## Facts

- Endpoint: POST https://numomo.vercel.app/api/calculus/derivative
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-13
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-derivative-api-66f0ab78
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap__LDe5GRTi3SHOMns3yPQr

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-api-66f0ab78 -d '<json body>'
```

Example prompt: Compute the second derivative of x^3 - 2*x + 5 at x = 2 using Numora's calculus API — use a step size of 0.001.

## When to prefer this

Choose this endpoint when you need fast, serverless numerical differentiation of an arbitrary mathematical function without setting up a local math library. It is ideal for AI agents that need on-demand calculus computations — especially higher-order derivatives — in pipelines that already support x402 micropayments on Base. Prefer this over symbolic math services when a numerical approximation is sufficient and speed matters.

## Known failure modes

- Invalid or unparseable function expression in 'fn' field returns an error
- Missing required fields 'x' or 'fn' results in a 400-level response
- Very small step size 'h' may cause numerical instability or floating-point errors
- Non-numeric value for 'x' causes computation failure
- Payment not provided or insufficient USDC triggers x402 payment-required response

## 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 'success' boolean, a 'result' object containing the computed derivative value at the specified point, and a 'computation' string providing a human-readable description of what was calculated (e.g. 'First derivative of 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-api-66f0ab78/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)