5.3 - 5.4

1) I'm confused about the connection between F, the antiderivative, and the integral of f.

2) Is there a systematic way of finding the antiderivative? We have all those nice formulas for finding derivatives..

as you know i wasnt there in class today. What was covered so that i can look at it in the book?

I think, i'm good with derivatives like this. can you put on another of the problems you had on the board today? or is that too difficult to do on the blog?

if thats the case, can you put on some related rates and optimization problems.

and, are there going to be limit questions on the test?

Solution to Problem 2

Here we will again make use of the product and chain rules:

By product rule =

. To find the two derivatives that we are looking for requires a triple application of the chain rule for each.

Now we have the arduous task of taking those derivatives:

= == = . Whew. Onto the next one. It's slightly easier.

==.

So our final answer is that

=
.

And that's it.

Solution to Problem 1

We will use the chain rule and product rule.

By the chain rule .

Now we must use the chain rule again.

. Now apply the product and sum rules to the last part.

= = .

Putting this all together gives the answer .

Some practice derivatives, per Nadav's request

Okay, compute the derivatives of the following functions:

1.


2.


3.

I will post solutions soon.

-Mr. Blumenfeld

A note on viewing comments

In order to the the see the comments for a post, you should click on the title of that post. That is all.

Practice problems

I'm finding that I'm having some difficulty simply recognizing which derivative rules i have to use on more complex problems. So for studying tomorrow night, can you put a bunch of problems on this blog and write the answers down. Because I'm not sure what I should be practicing, and i could just ask you something on the blog if necessary.

Test Post with TeX

Please let me know if this appears correctly on your computer:

TeX in Blogger

For those of you who are really adventurous with your desire to make things look nice in these blog posts, you can try to install this script to allow you to use LaTeX (pronounced Lah-tech), a program designed to do typsetting of math formulae. You will need to be running Firefox, and you'll need to learn to write in LaTeX, which is a little intimidating at first, but not at all bad once you get used to it.

The explanation of how to install it is here: http://wolverinex02.googlepages.com/emoticonsforblogger2

Note that the guy who wrote this also wrote a script to enable emoticons in blogger. That one is here:
http://wolverinex02.googlepages.com/emoticonsforblogger

Test Post

This is a test of the blogger account for AP Calculus. The goal here is to have a forum for people to discuss the topics that we are covering in class and be able to ask me and your fellow students questions regarding lecture topics and homework problems. We can also have people post their solutions here.

I'd like people to note that we need to come up with a convention to make typing math stuff easy. As such, I suggest using standard computer type notation. (e.g e^x means e to the x, * means times, / means divide, etc.)

If I can figure out how to put in TeX or equation editor here, I'll let you all know.