{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://www.calculatorx.com/schemas/math.numerical.derivative/1.1.4/input.json",
  "title": "Numerical derivative — input",
  "type": "object",
  "additionalProperties": false,
  "properties": {
    "method": {
      "type": "string",
      "description": "central/center/centred/centered; forward/fwd; backward/back/bwd; limit/lim/two_sided/twosided/two_sided_limit. Case insensitive; hyphens/spaces normalize to underscores."
    },
    "mode": {
      "type": "string",
      "description": "Alias of method; supplied aliases must agree."
    },
    "integrand": {
      "type": "string",
      "description": "poly/polynomial, sin, exp/e^x"
    },
    "f": {
      "type": "string",
      "description": "Alias of integrand; supplied aliases must agree."
    },
    "coeffs": {
      "anyOf": [
        {
          "type": "string",
          "minLength": 1,
          "description": "2–9 constant-first decimal coefficients; constants c0,0"
        },
        {
          "type": "array",
          "minItems": 2,
          "maxItems": 9,
          "items": {
            "anyOf": [
              {
                "type": "number"
              },
              {
                "type": "string",
                "minLength": 1,
                "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$"
              }
            ]
          }
        }
      ]
    },
    "coefficients": {
      "anyOf": [
        {
          "type": "string",
          "minLength": 1,
          "description": "2–9 constant-first decimal coefficients; constants c0,0"
        },
        {
          "type": "array",
          "minItems": 2,
          "maxItems": 9,
          "items": {
            "anyOf": [
              {
                "type": "number"
              },
              {
                "type": "string",
                "minLength": 1,
                "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$"
              }
            ]
          }
        }
      ]
    },
    "x": {
      "anyOf": [
        {
          "type": "number"
        },
        {
          "type": "string",
          "minLength": 1,
          "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$"
        }
      ]
    },
    "h": {
      "anyOf": [
        {
          "type": "number",
          "exclusiveMinimum": 0,
          "maximum": 1
        },
        {
          "type": "string",
          "description": "Finite positive decimal ≤1; explicit empty is invalid.",
          "minLength": 1,
          "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$"
        }
      ]
    }
  },
  "required": [
    "x"
  ],
  "description": "Forward, backward, or central finite difference of a polynomial, sin, or exp, plus a numeric two-sided limit. Discovery /two-sided-limit. Not symbolic d/dx. (calculation_version 1.1.4)"
}