I wrote this circuit because as we move into the chain rule, my students still don't have fluency with the product and quotient rules (boo!). So, this circuit really plays on functions that seem structurally similar but are very different... y = x^2 + cosx vs y = x^2cosx. Or, y = cos (x^2) as opposed to y = (cos x)^2 (of course without parentheses).
Students begin in the first cell and find either the first or second derivative (as specified) to advance in the circuit. The students then search for their answer and that cell becomes problem #2. Student proceed in this manner until they complete the circuit and return to the beginning.
* There are no logarithmic or exponential functions in this circuit. No implicit differentiation. No Inverse Trig Functions. *
My students love this format! The do not realize they are doing 16 (in this case) rigorous calculus problems. Try a circuit! You and your students will be hooked! Great for independent work, guided practice, class notes, you name it! Can be easily made into an around-the-room scavenger hunt or I Have / Who Has.
I do not include answer keys because the answers are embedded in the circuit. The teacher must work the circuit ahead of the students to see the idea unfold.