Post #2

Well, to begin, week two in my opinion was much more difficult that week one. At first we reviewed the stuff from the week before, and I understood everything like the quotient and product rules. Then the next day we did the arcsin stuff, and I understood how to do that. So I'm going to show and example of it. For the problem 2arcsin(x-1), you would have to use the formula arcsinu = (1/(sqrt 1-u^2)) times u^1. To start off, you just move the 2 into the next step without doing anything, then you put the rest of the problem into the formula, but do not forget to multiply it by the derivative of u, I've done that before. So, then you get (2)(1/(sqrt1-(x-1)^2)) (1), which you further simplify to make it 2/sqrt1-(x-1)^2, then in the next step you multiply out the (x-1)^2 to get 2/(sqrt(1-(x^2)-2x+1)), then your final answer become 2/ (sqrt( -(x^2)-2x-2)). I hope you could all understand that example, I tried my best to type it, but I'm not sure if I put all the parentheses and other stuff the right way. So I understood that, and the simple log problems, like how log27 9 = 27^x = 9, then you solve for x and you find that x=2/3. I also understand how you are supposed to expand log problems like, ln2/3 = ln2-ln3. The only problems I struggle with are the extremely long problems that you have to do loads of algebra and use like 7 different rules on different sections of the problem, for example,
-[sqrt((x^2)+4)/2x^2] -1/4ln[(2+sqrt(x^2+4))/x] one thing that helped me was writing down what you had to do for each part of the problem before you solve, like how for the first part of it, you need to use quotient rule, exponent rule, and work inside exponent; in the second part, you need to take care of the ln, then use quotient rule, then exponent rule, then work the inside exponent. But I suck at doing log problems like 10log4t/t because I suck at that kind of log stuff. I think you use quotient rule, and do all kinds of simplifying after that, but I just hate it.

mher---out.