So, this week was, once again, derivatives. I'm wondering when I'll be able to say something else... maybe I should just quit mentioning it at the beginning... I don't know. Knowing me, I'll forget what I say here by tomorrow anyways, so it doesn't matter much. Anyways, this week was a lot of u substitution and some deriving of functions themselves.
Taking the derivative of something like, say, x^2 + y^2 = 9 isn't bad at all. I think I got that stuff down pretty quickly, and I think (or, at least, hope) that shows through on the quiz today. I can do the whole y' thing and the factoring and division, that's not too bad. I think my biggest problem is the chain rule though, when you're dealing multiple functions within functions. For example, that stupid, stupid question on the quiz. sin^2[(2x-1)^4], if I remember right. I figured out that it was 16(2x-1)^3sin[(2x-1)^4]cos[(2x-1)^4], and I even simplified it further to 8(2x-1)^3sin[2(2x-1)^4], but I nearly forgot to multiply by that cosine at the end. I would've noticed it anyways, checking the answer on my calculator, but the point still stands that it can be incredibly easy to miss a small step and screw up the whole derivative. It's even worse when you take higher power derivatives, but we haven't had to deal with that. Yet. But, to get back to why that particular question is stupid, I spent about half an hour on it. With the correct answer. I didn't actually change anything from start to finish, I was simply poring over the work trying to find an error, any error that would throw it off. But no, my calculator decided that today was a good day to be inaccurate and refused to admit that I was right. Using the NDeriv function, I graphed what the calculator said was the derivative with what I said it was. I was way, WAY off most of the time, and I still can't figure out why, especially since I confirmed that I had the right answer in the end. Heck, I even went ahead and tried changing to cosine and doing it that way, only to arrive at the same exact answer. Really, really frustrating, especially since I spent so much time looking for something that wasn't there. But whatever, I guess I should be happy that I got the right answer, even if it did cost me a lot of time.
I'll be honest, that's pretty much all I have for this week. I think I had some ideas earlier, but that quiz pretty much eradicated any other idea I had, I needed to rant a bit more about it. In other news, we won a QuizBowl match through the strategic use of unexpectedly beneficial tactics, so I can't complain about how the week went in general. So it looks like this'll be all for tonight. Next update's gonna be on Friday, as always.