.. _auto_curve_slopeatx:

*COMPUTE THE SLOPE OF THE CURVE AT A GIVEN POINT*
=================================================

Computes the instantaneous slope (first derivative) of a curve at a specified X value, interpolating or extrapolating as needed. Use this worker when you need a single tangent/gradient value at a particular point along a curve.

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

Classification: **process**.

Tagged: ``curve``, ``derivative``, ``extrapolation``, ``interpolation``, ``slope``, ``slopeatx``, ``tangent``.

Inputs
------

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

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Curve To Be Looked Up
     - curvetobelookedup
     - vector
     - —
     - 
     - The input XY curve (vector of paired X/Y values) on which the slope will be evaluated; must be provided before the worker can execute.
   * - X Value
     - x_value
     - float
     - 0.0
     - 
     - The X coordinate (float) at which the slope is evaluated; the worker interpolates between adjacent points or extrapolates beyond curve bounds — defaults to 0.0.

Outputs
-------

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

   * - Label
     - ID
     - Type
     - Description
   * - curve_slopeatx_output_1
     - curve_slopeatx_output_1
     - scalar
     - Scalar slope value (ΔY/ΔX, same units as Y-axis units divided by X-axis units) of the input curve at the specified X position.

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_slopeatx <https://www.d3view.com/api/workflow/example?id=curve_slopeatx>`_

.. raw:: html

   <hr style="margin-top:2em">
   <p style="font-size:11px;color:#888">
   Auto-generated from <code>transformation</code> schema. Worker id: <code>curve_slopeatx</code>. Schema hash: <code>23e85913379c</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
   </p>