This week in AP Calculus we worked more on the chain rule, but we also were introduced to "u" substitution and implicit differentiation. With "u" substitution, the chain rule becomes a lot less of a mess, and it's easier to differentiate, and anti-differentiate because you can clearly see the "u" and "du". I still make mistakes when doing the chain rule with "u" substitution, but my understanding of it and ability to do it is improving. I think my main problem with "u" substituting comes from just basic problems with anti-differentiating (forgetting the +c and other things) and sometimes basic problems with the chain rule (choosing the wrong inside function), but I'm happy that it's getting better.
The other thing that was introduced that uses the chain rule is Implicit differentiation. Implicit differentiation is still a difficult topic for me. I only understand the process of it a little bit, which is the basic steps of treating one variable as a function of the other, so I can do basic problems involving it, but once it gets to a slightly more complex problem, I feel completely lost. Therefore, if I had to rate my understanding on the topic based on a scale of 5, I would give myself a 2, and a result of this was my struggle with the homework we were assigned on Thursday and Friday. However, because of this lack of understanding on the topic, I'm looking to study the subject a lot more because of the quiz on Monday. If left untended to, these problems are going to stack on top of each other and then finally crush me when the test day comes, so it's best to sort it out as early as possible.
The other thing that was introduced that uses the chain rule is Implicit differentiation. Implicit differentiation is still a difficult topic for me. I only understand the process of it a little bit, which is the basic steps of treating one variable as a function of the other, so I can do basic problems involving it, but once it gets to a slightly more complex problem, I feel completely lost. Therefore, if I had to rate my understanding on the topic based on a scale of 5, I would give myself a 2, and a result of this was my struggle with the homework we were assigned on Thursday and Friday. However, because of this lack of understanding on the topic, I'm looking to study the subject a lot more because of the quiz on Monday. If left untended to, these problems are going to stack on top of each other and then finally crush me when the test day comes, so it's best to sort it out as early as possible.