Post #2

So, my internet decides to work approximately 15 minutes before the blog is due (I've been trying for approximately 2 1/2 days). Lucky me! If it's late, don't blame me.

Ok, this week in Calculus was way harder for me than last week. I cannot simplify! Whereas last week was just the simpler stuff, this week we got into more complex, well, not concepts, but longer problems I guess you could say?

In the first week we learned how to take the quotient and product rules and how to take the derivatives of trig functions. For example, take the derivative of the following:

(x^2 - 2x + 4)/(x-4)

= (x-4)(2x-2) - (x^2 - 2x +4)(1) (quotient rule)
-----------------------------------
(x-4)^2

= (x^2 - 8x + 4)/(x-4)^2

This week, we also reviewed how to do logs before delving into the derivatives of logs. For instance:

Solve for x:

log39=x

All you do is switch it to so you have:

3^x = 9

and rather than taking the log of both sides like you would normally do, the answer is obviously x=2 because 3 squared equals nine.

We then went into taking the derivatives of natural logs, logs, and inverse trig functions. All I remember was that for the first night of homework (I think it was ln), I was really lost because even though I knew how to plug into the formulas, I just couldn't find out where to start or how to end it. But then I went to school and learned how to start. What really helped me was the list of things to do in the problem. And then I got a lesson in simplifying, and I got a little better. So, an example of inverse trig:

derivative of sin(arc cos(t))

= cos(arc cos(t)) * (-1)/(sqrt(1-t^2))

the cos and arccost cancel giving you:

t * (-1)/(sqrt(1-t^2))

which equals:

-t
--------------
sqrt(1-t^2)

For that particular problem, there wasn't much simplifying which is good for me. My only true problem is that I apparently cannot do basic algebra when simplifying.

And at the moment I'm going insane, so yeah, I think I'll end now.