This week was all about more u- substitution and implicit differentiation. Yay! More derivatives! Haha! When will this unit end? It's getting to be a bit much at this point but I'm getting through. I'm starting to really like doing derivatives, they're nice simple math, with definitive rules and regulations. They're amazing. You start to do u-substitution by identifying the u term, then you find u prime, then you make u prime match the rest of the problem, then once you've done all the necessary math, you substitute the original function back in in the place of u, then you've got your brand new derivative. I personally find this method to be unnecessarily difficult in that face of all the other methods we've learned, but whatever floats your boat. We also worked some more on the chain rule this week, which is probably one of the easier derivative rules so far. I didn't super understand it at the beginning but once we did more practice this week, I think I actually got it! The process for it makes way more sense and it's easier to recognize which function is the inside one and when a problem actually requires you to actually use the chain rule. Doing the multiple chain rules in one problem though can get kind of tedious if you ask, but still the end result looks nice.
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So this week was pretty low key. We took a quiz on Tuesday about the stuff we learned last week and then we learned about the chain rule. Now this was the first time I had ever heard of the chain rule. Which is defined by f'(g(x))*g'(x). Does not look too bad right? It isn't, at least it was not too bad on the worksheet we got right off the bat, but then when I got into the homework things start to get more complicated and everything just starts to look like alphabet soup. So I took a step back from the homework looked over my notes again, then took another stab at it, and it slowly but sure made a little bit more sense by the end of the homework assignment. I looked ahead at next week's lesson plans and I saw that we're working a little more with the chain rule so I'm hoping that as we work with it more and more I'll understand it enough to do well on the next quiz because grade needs some serious help if I'm gonna make it through this trimester... and the next two after that. This week we started derivatives. Well, I guess not started but definitely got into the meat of them. I was a little intimidated because sometimes when class gets into more advanced parts of the topic I can get really lost really fast but surprisingly enough I'm actually doing really well with derivatives and doing stuff with derivatives. Especially all the rules that go with derivatives. The only problem is, is that the algebra can get really tedious especially with the product and quotient rules being used in the same problem. I was really intimidated by the anti-derivatives, at least until Cresswell explained them. They're not too bad either. Another thing I was intimidated by was the three point five lesson because once you throw in sine and cosine, things can get real messy real quick but I took a quick look at the homework and it doesn't look to bad but I guess I'll find out this week and on Monday. But hopefully it won't be too bad or too long because I have to work all weekend and I really don't want to have to stress about this on Monday, which would be really nice. Who knows? This week end I'm either going to get a ton of stuff done or I'll have a lot to do on Monday. |
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January 2018
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