I wrote this circuit to give calculus students practice with reading and recognizing the limit definition of the derivative and then evaluating the derivative by using the rules of differentiation. So this would be after learning the power, product, quotient, and chain rules in addition to the trig and inverse trig rules, and exponential logarithmic rules. I would use this before I taught L'Hospital's rule.
There are 24 questions which build in complexity. The first two are done for the students to give them an idea of the thought process I would hope they would follow. Some of the questions students are finding a variable expression for the answer, in others they are finding numeric value.
No technology in needed nor should it be used.
My colleagues and I check our work very carefully but should you ever suspect an error or get stuck, please take a picture of the question and your work and email me at firstname.lastname@example.org.