We’ve started a new chapter in our calculus book -> Inverse functions.
After wondering a bit about how to approach this topic, I tried starting out in a different book, Spivak’s Calculus, which has a slightly more theoretical approach.
Now not sure how much the extra theory helped, but we did have a nice discussion about inverse functions this morning.
Tonight I wanted to give a few concrete examples and avoid the theory as much as possible. After a brief discussion, I started with the example of and found the derivative of the inverse function:
Next we moved on to and . He already has seen a bit of discussion about and its derivatives, so I let him play with the ideas about inverse functions to see if he could find the derivative of on his own:
Next up were the inverse trig functions. Today I chose to focus on and . I started by showing him and how basic trig relations produced a pretty surprising derivative:
Next up was . I let him try this one on his own, but I rushed into it too quickly and forgot to talk about the domain. That led to a bit of confusion at the end, but overall I was happy that he was able to get the general idea.