Chapter 48: The Product Rule For Differentiation: Situation 42 From the MACMTL–CPTM Situations Project
-
Published:2015
Heather Johnson, Shari Reed, Evan McClintock, Erik Jacobson, Kelly Edenfield, 2015. "The Product Rule For Differentiation: Situation 42 From the MACMTL–CPTM Situations Project", Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations, M. Kathleen Heid, Patricia S. Wilson, Glendon W. Blume
Download citation file:
In an introductory calculus classroom, a student asked the teacher the following question:
Why isn’t the derivative of y = x2 sin x just y ´ = 2x cos x ?
This Situation deals with a common student misconception that the derivative of the product of functions is the product of the derivatives of the functions. The Foci describe different ways of challenging this misconception and substantiating the true derivative of a product of functions. Focus 1 presents the slope of the tangent line as one way to think about the value of the derivative. In Focus 2, the definition of the derivative as a limit of a difference quotient is used to motivate the product rule for differentiation. In Focus 3, a property of even and odd functions and their derivatives contradicts the misconception.
