Differentiation I

“Differentiate $x^2$. Then differentiate $y^2$. Then $a^2$. Then $e^2$.”

This SWBQ can be implemented to test students' understanding of differentiation. When students differentiate a function, they do not usually ask “with respect to what.” This SWBQ is intended to confront students with the idea that when differentiating a function they first need to think about this question. This SWBQ also provides an opportunity for the instructor to find out what the students already know about differentiation.

Since most students remember something about how to differentiate a function, one can construct the answer on the front board from the bits and pieces that they remember, emphasizing why each of the pieces is important and talking about the process of differentiation.