Tuesday night was the Math Department’s second annual Derivative Bee, as well as my first visit to the event as a faculty volunteer.
Students participate in two categories. Category U is for students currently taking differential calculus (Math 131, 151 and 171). Category G is for students who have completed differential calculus (Math 152, 172 or higher).
In the first round, students are issued clickers and have 3-5 minutes to choose the correct multiple choice answer to a differentiation question. There wasn’t a lot for the faculty volunteers to do at this point, so I thought I’d play along. I was confident of my advantage; this isn’t the first time I’ve taught calculus. And I have those three magic little letters (Ph.D.) following my name.
It didn’t take long for me to get a little attitude adjustment. Question 1 was to evaluate
Since I don’t like using the quotient rule, I changed it to a product
and promptly made a distribution mistake in the multiple iterations of the product rule required to evaluate the derivative.
What I should have done in the first place was to FOIL out the product and divide through by the x in the denominator
which is just oodles easier.
Another problem I got schooled on: find the derivative of
Me? I love the chain rule, and the first thing I did was apply it incorrectly, not realizing that all those embedded square roots were also multiplied together and that the product rule is required, too! Fortunately, I caught my mistake and corrected it — with a not insubstantial amount of sweat. I was all proud of myself until one of the other instructors showed us the easy way to do the problem usingthe rules of exponentials.
which is an easy problem to solve!
This old dog learned a few tricks tonight. Including renewed respect for my colleagues and students. We have some smart people here at Texas A&M.