Calculate derivatives of familiar functions
I can apply the power rule for positive and negative integer and rational exponents
I can calculate the derivatives of sums and differences
I can apply the constant multiple rule when finding a derivative.
Quick Lesson Plan
The dot plots from a previous experience (Day 3) are still hanging on the walls of our classroom to remind students of the connection between the functions y = mx, y = x^2, and y = x^3 and their derivatives. Using this visual is a tremendous asset when introducing the Power Rule because the rule now seems more obvious: the conclusion of this rule is not a mystery to students. They have developed the power rule on their own! We introduce a few “intuitive” derivative rules by gradually increasing the complexity of the functions for analysis.
Continue to display the dot plots from yesterday’s work, if at all possible, and refer to their results often. The power rule is easily adopted by most students, as are the rules for constants, sums and differences, and constant multiples of functions. Combining rules requires students to write legibly (a struggle for some!) and keep their terms and expressions organized. When the power rule is used in concert with the product rule, or a root must be rewritten as a rational exponent, creative “MAL-gebra” might appear. Some review of Algebra 2 concepts might be required today. Provide enough practice for students so that navigating between positive and negative, integer and rational exponents.
These rules must be memorized, practiced and mastered before the AP Test. These skills are woven throughout the multiple choice and FRQ sections of the test. The more practice we provide, the more efficiently students will complete these derivatives!