Exercise for Wednesday

At the end of today’s class we saw that we could use to prove that the derivative of is . Try using this fact to determine the derivative of , where is any positive number.

Hint 1: There’s a clever way to rewrite that will help you see what to do.

Hint 2: Remember how, given , you were able to evaluate, for example , where is just some number? Try using that knowledge to evaluate . Then try to see how this actually helps you differentiate .

This exercise is technically optional, but I think you might like to think about it and play around before Wednesday’s class, even if you don’t get anywhere. If you’d like to share what you came up with, you’re welcome to write it on the board before class. You can also post a comment here, but try not just posting your answer until Tuesday night or so…it’s less fun for the others to work on it if you’ve already spoiled the answer for them!