Day 6: "Guess the Derivative"

In "Guess the Derivative", I assume that the students need a reminder of where the graphs of sine and cosine came from. I may even start with an explanation of the unit circle if they had one of those pre-calc teachers that helped them memorize the unit circle but not actually learn it. We go over the graph of sine using the angles at 0, pi/2, pi, and 3pi/2 and then filling in the extra points. Same for cosine. Then I have them remind me what they learned yesterday about what a derivative is. Then we start plotting the slopes and deriving the derivatives of both trigonometric functions. It is so fun! They have never thought about graphing slopes before! It is an honor to be the one who gets to show them how to do that.

On a side note, one year I had an A-student literally CRY when she found out the derivative of sine was cosine! I'm still baffled by her, but that story still makes me laugh.

Anyway, the lesson starts with easier derivatives and then builds its way to sine and cosine. The last derivative we discuss in this lesson is e^x.

Again, the reason I do all of this so early in the year is so that I can have them do L’Hôpital in the limits unit. If you think about the limit questions they do see on the AP exam, like half of them are L’Hôpital.

Anyway, from this point on I teach calculus the same way most everybody does.