Derivatives: a guide to calculation

Overview

The calculation of derivatives is a key topic in all differential calculus courses, both in school and in the first year of university. It’s also an essential tool used continuously in advanced courses, not only in Mathematical Analysis but in many technical and scientific subjects. Last but not least, derivatives are the fundamental tools of all optimization algorithms, including those used in machine learning and deep learning. This course aims to teach the techniques and rules for calculating the derivatives of any function in a simple yet comprehensive way, ensuring zero mistakes! Lessons are packed with examples and visuals to clarify techniques, along with exercises to reinforce learning. Additionally, we explore the integration of Geogebra and Wolfram Alpha to enhance understanding of derivatives and support calculations, and show how ChatGPT can create dynamic learning experiences and personalized practical sessions. The course includes video lectures (Week 1), solved exercises (Week 2), in-depth notes (Week 3), tutorial for using the digital tools (Week 4) and a final self-assessment quiz.

Syllabus

Week 1 - Derivatives

In this week, you'll find 9 video lessons on the concept of derivatives, their geometric interpretation, elementary derivatives, and the rules of differentiation.

Week 2 - Suggested Exercises

In this week, you'll find a video-exercise and 11 exercises, complete with detailed solutions, which you can work on independently to strengthen your skills. These exercises are not graded.

Week 3 - Insights

This week, you'll find some extra insights on derivatives to help you dive deeper into the topic. Make the most of it to boost and broaden your knowledge!