I wrote this worksheet for my students to understand "where the quotient rule comes from," in terms of rewriting the original quotient as a product of a function, and another "to the negative one" power.
Students enjoy seeing how the result "pops out" of their algebra; they do sometimes struggle, however, with applying the chain rule to the function which was "raised to the negative one power."
So that students can see that their answers "work," instead of having them check their answers against a key, I have them use the dy/dx functionality of their TI graphing calculators to verify that they have indeed found the correct derivatives. Of course, the obstacle in using this method is that they struggle with getting their parentheses in the right places, but I figure it's good practice for them to learn to do it correctly!
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
For this worksheet, I expect students to show their work on a separate sheet of paper.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.