HigherOrder Derivatives and Derivative Strategies (Topics 3.53.6)
Unit 3  Day 9
Learning Objectives

Choose appropriate strategies for evaluating derivatives

Determine higher order derivatives of a function
Success Criteria

I can select and apply a combination of derivative rules

I can recognize higher order derivatives in various notations

I can calculate higher order derivatives
Quick Lesson Plan
Overview
We are finishing off the chapter with a group activity called Round Robin. Strategically choosing derivative rules and calculating higher derivatives requires exposure to such problems. Positive interdependence among group members is fostered by doing work that relies on the previous work of a group member.
Teaching Tips
In this activity students are grouped in pods of four. Each group member receives a different sheet (Problem Set A, Problem Set B, Problem Set C, and Problem Set D) and works on question #1 only. Set the timer for 4 minutes. The first problem is the easiest and should take the least amount of time. At the end of the four minutes, have students pass the paper to the next person. Each student will now 1) read the new prompt, 2) check the work done by their team member on question 1, and 3) do question 2. In many of the problem sets, subsequent questions rely on previous answers (like calculating the second derivative after the first person has already calculated the first derivative). For round two, set the timer for 8 minutes this time since students have to check their group member’s work AND solve a slightly more complex problem. Repeat this process 2 more times (12 minutes for round 3 and 15 minutes for round 4). At the end, each student should get back their original paper. They should review the answers, check for accuracy, and ask their group members any questions they may have. Remind students that they need to know how to do all of the types of problems, not just the ones they completed themselves, which should encourage further discussion among the students.
Exam Insights
The AP Exam varies the notation used for higherorder derivatives. This activity mixes in both Leibniz and Newton notation so make sure your students are familiar with both.
The AP exam loves to mix derivative rules in FRQ questions. Students should not be surprised to find the chain rule, product rule, and quotient rule in the same question. (See 2016 AB6 and 2017 AB6). Students should also be prepared to interpret functions given in multiple representations.
Problem Set C is a slightly modified version of 2015 AB6!
Student Misconceptions
Some of these problems are quite tricky! In Problem Set A, simplifying the derivative significantly decreases the complexity of finding the next derivative. It is important for students to be able to recognize when simplifying is useful and when it is unnecessary.