{"uid":"cap__LDe5GRTi3SHOMns3yPQr","slug":"numora-calculus-derivative-api-66f0ab78","name":"Numora Calculus Derivative API","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://numomo.vercel.app/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":"registry","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":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_5RFX8uhbzASXyOzc1K59B","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the numerical derivative of a mathematical function at a specified point, with support for higher-order derivatives and configurable step size.","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Slope of a curve at a point","prompt":"What is the derivative of sin(x) * x^2 at x = 1.5? I need the exact numerical slope of that curve at that point."},{"title":"Higher-order derivative for physics simulation","prompt":"Calculate the second-order derivative of the function 3*x^4 - x^2 + 7 evaluated at x = 2, so I can use it in my acceleration model."},{"title":"Optimization gradient check","prompt":"I need to verify the gradient of my objective function f(x) = exp(-x^2) at x = 0.5 — can you compute the first derivative numerically with a step size of 0.0001?"}],"resultDescription":"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').","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-13T18:48:00.937Z","isFirstParty":false}