In calculus, I’ve historically asked kids to take the derivative of:
and students will immediately go to the quotient rule. OBVIOUSLY! There’s a numerator and denominator. Duh. So go at it!
Unfortunately, this is VERY UNWISE because it leads to a lot more work. And I was sick of my kids not taking a moment to think: what are my options, and what might be the best option available? Also, kids generally found it hard to deal when we started mixing the derivative rules up!
So I came up with a sheet to address this and paired kids to work on it.
(I’ve also had kids think they can do some crazy algebra with . This sheet also helped me talk with kids individually about that.)
For a little context, my kids have only learned the power rule, the product rule, the quotient rule, and that the derivative of is . They have not yet been formally exposed to the chain rule.
Without further ado…