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Multivariable Calculus: Derivatives

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Curriculum Module

Created with R2026a. Compatible with R2026a and later releases.

Information

This curriculum module contains interactive MATLAB® live scripts that teach and apply standard concepts for multivariable derivatives.

Background

You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. This module covers partial derivatives with applications to machine learning and computer vision.

The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the EndIcon.png Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Contact Us

Contact the MathWorks teaching resources team if you would like to to request assistance, provide feedback, or if you have a question.

Prerequisites

This module assumes knowledge of single variable calculus, vectors, including vector fields, and matrices, including determinants, as covered in the courseware listed here:

Courseware Module
Sample content
Available on:
Matrix Methods of Linear Algebra
MatrixCard.png
OpenInFX.png
OpenInMO.png
GitHub
Calculus: Derivatives
ProductRuleCard.png
OpenInFX.png
OpenInMO.png
GitHub

Getting Started

Accessing the Module

On MATLAB Online:

Use the OpenInMO.png link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.

On Desktop:

Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double-click Derivatives.prj. It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start.

Ensure you have all the required products (listed below) installed. If you need to include a product, add it using the Add-On Explorer. To install an add-on, go to the Home tab and select AddOnsIcon.png Add-Ons > Get Add-Ons.

Products

MATLAB® and Symbolic Math Toolbox™ are used throughout. Tools from the Image Processing Toolbox™ are used in the computer vision example. The function randsample from the Statistics and Machine Learning Toolbox™ is used to create Exercise 5 in the partial derivatives script.

Scripts

SeaSurfaceGradient.png
In this script, students will...
$\bullet$ Compute and visualize partial derivatives, directional derivatives, and gradients
$\bullet$ Recognize notation for partial derivatives
$\bullet$ Apply the chain rule for partial derivatives
Academic disciplines
$\bullet$ Machine learning (gradient descent)
$\bullet$ Mathematics
$\bullet$ Computer Vision

License

The license for this module is available in the LICENSE.md.

Related Courseware Modules

Courseware Module
Sample Content
Available on:
Multivariable: Space and Functions
ShapesCard.png
OpenInFX.png
OpenInMO.png
GitHub
Multivariable: Integrals
LineIntegral.png
OpenInFX.png
OpenInMO.png
GitHub
Applied Partial Differential Equations
PDEShockCard.png
OpenInFX.png
OpenInMO.png
GitHub

Or feel free to explore our other modular courseware content.

Educator Resources

Contribute

Looking for more? Find an issue? Have a suggestion? Please contact the MathWorks teaching resources team. If you want to contribute directly to this project, you can find information about how to do so in the CONTRIBUTING.md page on GitHub.

© Copyright 2026 The MathWorks, Inc

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Interactive scripts that teach partial derivatives.

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