Week seven has been pretty okay. We talked about the chain rule. It’s probably the most annoying rule yet but it isn’t that bad. It kind of makes sense because it’s just taking the derivative of the outside while leaving the inside alone and then multiplying that by the derivative of the inside. It’s really annoying when you have to simplify that but we don’t usually have to do that so I guess it’s okay. It’s basically been expanding our knowledge about derivatives so we have the background knowledge which really helps. Sometimes I still struggle with finding the derivatives of things so that’s still not fully there. Sometimes I’ll get all the way to the end of a problem and then I’ll realize I messed up finding the derivative earlier on and then I just scream a little. It’s annoying because it always happens when I’ve actually simplified the problem and it’s just the worst. But yeah it’s pretty easy and painless so I’m not sure what else to say about it.
Week 6 is done and with that I’m ⅙ of the way done with this class. This week we talked more about the rules for finding derivatives. These rules made everything so much easier. Like couldn’t we have known about these sooner? No we had to do things the hard way first. I’m starting to feel like all math teacher like to torture us with complicated things when there are easier ways to do it. My dad does this too! Ugh, math teachers. Anyway the rules for derivatives are pretty nice. Other than the quotient one. That one kind of sucks but it’s still easier than having to use lim h->0 of f(x+h)-f(x)/h. That thing really sucks. I understood everything we did this week. It was pretty straight forward. The power rule is going to be in a picture down below because I don’t really feel like trying to write it out. It’s really easy though so that’s really nice. The product rule is f*g’+f’*g. Pretty easy. The quotient rule is (the derivative of the bottom times the top)-(the derivative of the top times the bottom)/the bottom squared. Not as easy but still not too bad.
So it’s week 5 already. Only one more week until the end of the marking period. Only one more week until I’m ⅙ of the way done with this class. Yay! This week we talked about derivatives. They seem fairly simple. I mean they can be a lot of work with the 4 step process but oh well, at least it’s easy work. I thought it was kind of funny when Cresswell broke down the derivative equation thing into the four steps. At first I thought it would be some like big, crazy, helpful thing but nope. It was literally the equation broken up into its components. I still wrote it all down though. I started it so I had to finish it.
The 4 steps are:
The exercise at the beginning of the lab helped me see how a slope of a point is related to a function. This made making the GIFs a little bit easier. Having a basic knowledge of what was happening made it so that Kathryn and I were able to get the first GIF done with only a little bit (or a lot) of confusion and crying. Then came the second GIF. Oh how I hated the second GIF. After almost an entire period of messing with variables and punching the computer, I decided to google it. I decided that the best thing to google was “Connor Jones AP calc blog” and man was that a good idea. I could find his equations and as soon as I saw them I thought to myself “How did I not figure that out?” It made so much sense once I saw it. I probably couldn’t figure it out myself because I was tired and I had been working on the same thing for an hour. But now that I know what to do everything makes sense. Once I had that done, making my own GIF was pretty easy. I just followed the same basic steps and BAM! GIF. Secant lines are the average rate of change of a function. Tangent lines are the derivative of a function.
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