Scribe Post. 10/18

Today in class Mr. O'B calmed everyone down by telling us to not stress about the quiz, because as long as you don't consistently bomb every quiz during the quarter, the grades won't effect you too much. Next we took a look at  Caleb's Scribe Post from the previous class. Next we learned the best news we've received in class all year. There is an answer book that show the work to every problem. And Mr. O'B owns it! Although you can't take this book out of class, you can come in after school, during study halls, or take a peak at it during class. We are reminded although it has the solution and the work for the solution to every problem its not always the best way to get to the solution.
Heres a nice picture of the glamorous book.

Then we took a look at the Questions for Class, there were so many but the awesome thing is that Mr. O'B answered every single question on there. Go on and take a look and surely everything will now make since to you. Heres the link Questions for Class. Also while looking at those we saw that another student answered as -a friend, on their. Mr. O'B of course being a busy man would probably love if classmates would answer questions for other classmates, if you do so you get a nice little IOU. So monitor that site cause I know I'm always looking for some help!

Next we took the 2nd Quiz of the 2 Unit of the Quarter. That ended around 10:30 and we were off to looking at some new material. 

Written on the board was:

Problem: I know how to take the derivative of the square root function and I know how to take the derivative of a linear function. I can take the derivative of their sum or difference and even of their product or quotient. But how do I take the derivative of their composition?? I mean, whats ?!?!!? Bluester with a smile on his face whispered SOL a couple of times... which if I am correct= sh*t out of luck

Then we went over to the other side of the board and saw that Mr. O'B had written down some equations on the board during the class. Written was problem #43 from IW#6. 

=

Suddenly we were stopped. We know the derivative of cos and we know the derivative of 2x, for this problem. But this was the Damien Rule Tricker. If you use the Damien rule its powerful but doesn’t allow you to take the derivative rule. We were than told walking out today we can find the derivative of every single function. Exponential and logarithmic are the only ones we can’t take derivative algebraically. Then we were appointed to the Chain Rule!

The Chain rule is huge! In words the Chain Rule states is The derivative of the OUTER function evaluated at the INNER function times the derivative of the INNER function. Heres a link to a video about the rule, from our friend PatrickJMT. 

Also here is a picture proof for the chain rule.

http://www.onemathematicalcat.org/NAU/Calc1_MAT136/indexCards/card23.jpg don't want to plagiarize so here

Now going back to #43 from IW #67 using the Chain Rule 

We saw that 

Then we tried the chain rule with the question from U2Q2 #5
   At x=1


Now we can reduce that down to 

Then since x=1 we plug in 1 

Final Answer: 

Next we looked at U2Q2 #6
This is a composite function. 


Now into the trusty chain rule invented by Sir Issac Newton



Now reduced down to 


Then we did another example heres a little image to show the step of the example.

After viewing these different examples of the chain rules, you see that this is a much better method then the quotient rule, you are more likely to make a mistake when you use the quotient rule. Things to always remember with the chain rule is to always take the derivative of the chain of g(x) thats has to be multiplied there, thats a common mistake. Appreciate these rules because now we don't have to use the limit definitions!
To end the class we found another crafty way to show the chain rule in Leibniz notation, if
 and , then


where

 is evaluated at 
It is like the  cancel away in this notation.
During the class of 10/19 we went over a couple of notes here are the pictures. 

These pictures are both from #23 on IW #7, on the top its the example of how to go about it and on the bottom picture its actually the work to do it. 

Also below is another version of the same problem worked out on the board, pretty much written the same exact way just another visual thats bigger to read. 

After this we worked on our IW's individually for the rest of class. 

At this point the bell had rung and it was the end of class and the IW#7 for today is p. 158/15, 17, 19, 23, 27, 29, 33, 39, 53, 55, 58, 72, 73
Post the questions up if your having problems and who knows maybe someone will get an IOU, win win sit

Scribe for next Red Day 80 minute class. A Crans!

Update: If you are still struggling with the chain rule on the quizzes or the homework and want to take a look at a nice example before the quiz, this LINK is the one that you will want to watch. It gives an easy to follow example of the chain rule with all the work being displayed with commentary that is very nice and professional. 
We have seen a lot for chain rules throughout the quarter with different material, but as lately we have been using a lot of  lately in the IW's, here is an example we did on the board using the new .