{"uid":"cap_ZZTkEj7zkMx-O7J9k3PN7","slug":"numora-calculus-derivative-endpoint-53dbdddd","name":"Numora Calculus Derivative Endpoint","description":"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.","url":"https://numorapoi.orbonomy.xyz/api/calculus/derivative","method":"POST","headers":{},"bodySchema":{"type":"object","required":["x","fn"],"properties":{"h":{"type":"number"},"x":{"type":"number"},"fn":{"type":"string"},"order":{"type":"integer"}}},"responseSchema":{"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"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.04/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.04","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.04","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_w6CCrHtFX-d16y7mVabpj","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.04","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the numerical derivative (first or higher order) of a mathematical function at a given point","exampleAgentPrompt":"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.","exampleUseCases":null,"resultDescription":"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').","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T12:31:35.653Z","isFirstParty":false}