Calculus Derivatives
Curriculum Module
Created with R2021a. Compatible with R2021a and later releases.
This curriculum module contains interactive MATLAB® live scripts that teach fundamental concepts and basic terminology related to derivative calculus. There is a focus on numerical approximation and graphical representation as tools for understanding the concepts of calculus.
You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside of class. The derivatives module is divided into five scripts and a practice app. The first covers the limit definition of the derivative and includes several motivating examples for the study of derivatives. The second covers derivatives of powers and the linearity of derivatives working from the limit definition of the derivative, including an application to parabolic motion. The third covers derivatives of exponentials, natural logarithms, sines and cosines as well as discussing higher order derivatives. Applications include population growth and oscillatory behavior. The fourth script presents visualizations of the product and chain rule for derivatives as well as randomly generated practice problems. Applications include related rates and the quotient rule for derivatives. The fifth script presents approximation of differentiable functions by polynomials, including tangent lines, and leading up to Taylor polynomials. The Calculus Flashcards app allows users to select the types of derivative (or integral) rules they wish to practice, generate randomized problems, and track their progress within a session.
The instructions inside the live scripts will guide you through the exercises and activities. All interactive exercises offer feedback while reflection questions are more openended and do not include solutions in this module. 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 Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.
Solutions are available upon instructor request. Contact the MathWorks teaching resources team if you would like to request solutions, provide feedback, or if you have a question.
Mathematically, this module assumes a knowledge of functions that is standard in precalculus course materials regarding powers, exponentials, absolute values, logarithms, sines, cosines, rational functions, and asymptotes. In addition, this module assumes basic fluency with limits in discussing the limit definition of the derivative.
Minimal MATLAB fluency is required to use this module; primarily it is standard calculatortype mathematics such as using \texttt{*} for multiplication and / for division. For commands that go beyond interacting with a calculator, the necessary knowledge is included in the module. If you want to improve your MATLAB knowledge, MATLAB Onramp is a free twohour introductory tutorial that teaches the essentials of MATLAB.
Use the 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.
Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts and doubleclick on 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 AddOn Explorer. To install an addon, go to the Home tab and select AddOns > Get AddOns.
MATLAB® and the Symbolic Math Toobox™ are used throughout. Tools from the Curve Fitting Toolbox™ are used in TranscendentalsRules.mlx.
TaylorPolynomials.mlx  In this script, students will... 

 compute tangent lines.  compute quadratic approximations.  compute higher order polynomial approximations. 
App: Calculus Flashcards
Practice recognizing and solving standard computational problems in calculus.
The license for this module is available in the LICENSE.md.
Courseware Module  Sample Content  Available on: 

Calculus: Integrals 
GitHub 

Fourier Analysis 
GitHub 

Numerical Methods with Applications 
GitHub 
Or feel free to explore our other modular courseware content.
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 2023 The MathWorks™, Inc
Cite As
Emma Smith Zbarsky (2024). Calculus Derivatives (https://github.com/MathWorksTeachingResources/CalculusDerivatives/releases/tag/v1.3.0), GitHub. Retrieved .
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