{"uid":"cap_FmauKtX1tzOQyaAk0-tEb","slug":"numora-calculus-derivative-endpoint-9184d183","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://numormo.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_M8PQAVfpoJs0MHJoynq2a","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":"Numerically computes the derivative of a mathematical function at a specified point, supporting higher-order derivatives.","exampleAgentPrompt":"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?","exampleUseCases":[{"title":"Optimization gradient computation","prompt":"I need the derivative of f(x) = x^4 - 5*x^2 + 4 evaluated at x = 1.5 so I can find out the gradient direction for my optimization step."},{"title":"Physics rate-of-change check","prompt":"What is the instantaneous rate of change — so the first derivative — of position(x) = 3*x^2 + 2*x - 7 at time x = 4 seconds?"},{"title":"Higher-order curvature analysis","prompt":"Calculate the third derivative of sin(x) at x = pi/6 with h set to 0.0001 — I'm checking the curvature behavior of the function."}],"resultDescription":"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').","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T19:05:11.819Z","isFirstParty":false}