.. _auto_curve_derivative:

*COMPUTE THE DERIVATIVE OF THE CURVE*
=====================================

Computes the numerical derivative of a curve, supporting higher-order successive derivatives and optional pre-processing steps such as x-monotonic cleaning and digitization. Use this worker to obtain velocity from displacement, acceleration from velocity, or any nth-order rate-of-change signal.

When to use
-----------

Classification: **process**.

Tagged: ``curve``, ``derivative``, ``differentiation``, ``digitize``, ``monotonic``, ``nth-order``, ``signal``, ``transformation``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve To Be Derived
     - curvetobederived
     - vector
     - —
     - 
     - The input X-Y curve (vector) to be differentiated; supply as a d3VIEW curve object — this is the primary signal on which the derivative is computed.
   * - Num Succession
     - num_succession
     - scalar
     - 1
     - 
     - Order of differentiation (integer ≥ 1); defaults to 1 for a first derivative, set to 2 for a second derivative, etc.
   * - X-Monotonic
     - x-monotonic
     - scalar
     - no
     - 
     - Set to 'yes' to pre-process the curve so that x-values are strictly monotonically increasing before differentiation; default is 'no'.  Enable when the raw signal contains duplicate or out-of-order x-values.
   * - Digitize
     - digitize
     - scalar
     - -1
     - 
     - Number of evenly-spaced points to re-sample (digitize) the curve to before computing the derivative; default is -1 (disabled). Set to a positive integer to resample first.
   * - Overlay Derivative
     - overlay
     - scalar
     - no
     - 
     - Set to 'yes' to overlay the derivative curve on top of the original input curve in the output plot; default is 'no'.

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - curve_derivative_output_1
     - curve_derivative_output_1
     - vector
     - The resulting derivative curve (X-Y vector) after applying the requested order of differentiation and any pre-processing; x-axis units match the input, y-axis units are input y-units divided by input x-units per derivative order.

Disciplines
-----------

- data.curve.transform
- data.signal_processing

Runnable example
----------------

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=curve_derivative <https://www.d3view.com/api/workflow/example?id=curve_derivative>`_

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>curve_derivative</code>. Schema hash: <code>3a7117c3d846</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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