The main focus of this week was the Chain Rule and continuing to work with derivatives. I have really liked derivatives so far! I am a little nervous for Monday's lesson where we will be learning to find anti derivatives with the chain rule, but I don't think it will be too bad after some practice. I also think the videos on the weebly site with help a lot. I like being able to take notes from videos because it is nice to have the option to pause and go back in the video if something was missed.
Before we learned about and began working with the Chain Rule, we took the 3.3 and 3.5 Quiz. I think it went pretty well and I feel really good about everything it covered. One problem I had trouble with was the one where we needed to prove that d/dx cot x = - csc^2 x. I confused my thought process with the way we did proofs that we focused on last year in trig with trig identities. I should have practiced these proofs more before the quiz, but now I understand that they do not only involve substitution and simplification, but also using the rules for derivatives. Here I have worked out the problem that I missed on the quiz and it makes a lot of sense now that I used the quotient rule: |
A lot of times I can get frustrated with the activities and labs that we work on when we are introduced to a new concept, but in the end these activities are what always help me to achieve a deeper understanding of what we are learning. This week's activity asked us to look at patterns and form our own conjectures of how the Chain Rule works. Forming our own ideas of what the rule might be based on our exploration in the activity was very helpful when it came to learning the Rule in the lesson. As I was working on the homework, I found that one concept that wasn't completely clear to me was how to use the chain rule with functions that are composed of more than two functions, or had multiple "inside" functions. Working through these problems in the homework and practicing some in class on the whiteboards has helped me to clear up my confusion and fully understand how the Chain Rule works with different types of problems.