> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Evaluate Cubic Spline Derivative

> Construct a cubic spline and evaluate its derivative at a given point. The derivative of a cubic spline is a quadratic spline that is continuous (C1). Useful for computing forward rates from zero rates, implied volatility slopes, and sensitivity analysis. [Tier: BASIC, Credits: 1]



## OpenAPI

````yaml api-specs/numerical.json post /quantlib/numerical/interpolation/spline-derivative
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Numerical
  description: >-
    Numerical module endpoints for FinceptQuantLib API. The Numerical module
    (Basic Tier, 1 credit per request) provides comprehensive numerical methods
    including finite difference differentiation, Fast Fourier Transform (FFT),
    numerical integration (quadrature and Monte Carlo), interpolation methods
    (linear, cubic, spline), linear algebra operations (matrix decomposition,
    solving systems), ODE solvers, root finding algorithms, optimization
    methods, and nonlinear least squares fitting. Essential for quantitative
    analysis, scientific computing, and numerical model implementation.
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-numerical
    description: >-
      Numerical methods including differentiation, FFT, integration,
      interpolation, linear algebra, ODE solvers, root finding, and optimization
    x-displayName: Numerical
paths:
  /quantlib/numerical/interpolation/spline-derivative:
    post:
      tags:
        - quantlib-numerical
      summary: Evaluate Cubic Spline Derivative
      description: >-
        Construct a cubic spline and evaluate its derivative at a given point.
        The derivative of a cubic spline is a quadratic spline that is
        continuous (C1). Useful for computing forward rates from zero rates,
        implied volatility slopes, and sensitivity analysis. [Tier: BASIC,
        Credits: 1]
      operationId: spline_derivative
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - x_data
                - y_data
                - xi
              properties:
                x_data:
                  type: array
                  items:
                    type: number
                  description: X coordinates of data points
                  example:
                    - 0
                    - 1
                    - 2
                    - 3
                y_data:
                  type: array
                  items:
                    type: number
                  description: Y coordinates of data points
                  example:
                    - 0
                    - 1
                    - 4
                    - 9
                xi:
                  type: number
                  description: Point at which to evaluate the derivative
                  example: 1.5
                bc_type:
                  type: string
                  description: Boundary condition type
                  enum:
                    - natural
                    - clamped
                    - periodic
                  default: natural
                  example: natural
            example:
              x_data:
                - 0
                - 1
                - 2
                - 3
              y_data:
                - 0
                - 1
                - 4
                - 9
              xi: 1.5
              bc_type: natural
      responses:
        '200':
          description: Successful Response
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      xi:
                        type: number
                        description: Point of derivative evaluation
                        example: 1.5
                      derivative:
                        type: number
                        description: Derivative value at xi
                        example: 3
              example:
                success: true
                data:
                  xi: 1.5
                  derivative: 3
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientTierError'
        '422':
          description: Validation Error
      security:
        - APIKeyHeader: []
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientTierError:
      description: API tier insufficient for this endpoint
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Endpoint requires Basic tier or higher
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````