This week we started talking about the anti-derivative version of the Chain Rule.... "U" Substitution. We also talked about the topic of Implicit Differentiation towards the end of the week. They were both just expanding upon the idea of derivatives and differentiation so I guess it shouldn't be that hard if you fully understood the past concepts. So basically spent the whole week learning and reviewing for the upcoming quiz on Monday about this stuff.
"U" Substitution is when you identify which is the inside part of a chain rule derived function and substitute the letter "u" for that whole part. Then, find the derivative of that inside function and label it as "du" and substitute that in also. It gets kind of convoluted when you start getting a constant or a term that does not match what the original derived function has so then you would have to divide to have "du" or "dx" alone then substitute them back in. After learning this rule for the first time, I was lost as heck. I understood it to the substitute for "u" part, but then when it came to the "du" stuff, I got lost. But, i think doing the homework and more practice has helped me understand it better. Expecially the mini quiz that we did half way through the week to check our understandings on Chain Rule, "U" substitution, and anti-deriving in general.
The next topic that we learned and talked about what Implicit Differentiation. This is basically saying that you have to derive both sides of an implicitly defined equation. For example, in y^2=x you would start with having 2y*dy/dx=1. This is because you derive both the left and the right side. But the catch is that whenever you derive something with a variable y in it, don't forget to use dy/dx for it. The main objective of this is to collect all terms with dy/dx's on them to one side then go from there. It doesn't get any different when we start talking about high order derivatives for implicitly defined functions, because the only difference is that you would have to do it twice and substitute the value for dy/dx back for the answer if you need it. This was way easier to understand than the "u" substitution, but I guess it's because it's more of just basically a collection of everything that we've been doing so far and less of new concepts.
I feel like I'm going to be more or less ready for the upcoming quiz on Monday, I just need to practice more during the weekend.
Bryll Matthew Moreno