Overview

Students will work through eight stations to review several methods for finding derivatives, with a focus on rational and root functions. 

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Teaching Tips

You may choose to have students work with a partner on the stations and move to the next station whenever they are finished, or you can assign a group to each station and then have all groups switch after an allotted time (4-5 minutes), rotating through all eight stations, as time permits. Challenge students to identify and use multiple methods for finding derivatives such as simplifying the function or writing the function as a product or quotient and applying the appropriate rule. 

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Exam Insights

Algebra errors abound when finding the derivatives of root and rational functions. Students often confuse fractional exponents with negative exponents and often get stuck re-writing the function in order to get it power-rule ready. If simplifying the function is complex, some students forget to take the derivative altogether. Encourage students to properly label their work, clearly delineating between f(x) and f’(x), as well as the general derivative function f’(x) and the derivative evaluated at a point (e.g. f’(3)).

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Student Misconceptions

Unit 2 lays the groundwork for a wide variety of derivative problems students will see on the AP exam, including limit problems that can be solved with the definition of the derivative. Having derivative rules memorized for the six trig functions and properly executing the product and quotient rules are crucial for non-calculator portions of the exam as well as tabular questions where the function rule is not known.