Scribe Post Friday October 15, 2010

We began class with a quiz. Mr. O'Brien reminded us again we will get a lot of partial credit, and there will most likely be a curve because of the difficulty of the quiz. Remember we have until May to get a good grasp on the whole Calculus thing.

Remember to keep working on memorizing these things if you haven't already:

1) Trig values
2) 6 Trig derivatives
3) Product Rule
4) Quotient Rule
5) H-->0 form and x-->c form

After the quiz we began talking about the chain rule. We started by working on a worksheet (Exploration 3-7: Rubber-Band Chain Rule Problem). Everyone worked together in groups on this for a few minutes, then Mr. O'Brien took over and went over this with us all as a class. The answers are all published on the Blog.

Some key concepts that we learned from this was:

dx/dt This means "the derivative of x with respect to t." Also, dx is the rise, and dt is the run, which means it is the slope.

Next, we learned a second form of the chain rule:

If y is a function of u and u is a function of x then:

dy/dx=dy/du*du/dx

Using this we re-looked at question 1 from the quiz we took earlier in class.

y=cos5x

y=cosu and u=5x

So,

dy/du=-sinu and du/dx=5

dy/du=dy/du*du/dx

=-sinu*5

=-5sin5x

After going over the worksheet and the example from the quiz we went onto grapher and Mr. O'Brien showed us an odd function. He then showed us that the derivative of a odd function is an even function. For example: The derivative of x^2 is 2x, and the derivative of x^3 is 3x^2.

Prove: The derivative of any odd function is even

Proof: f(-x)=-f(x)
Take derivative of each side

f'(-x)*-1=f'(x)

Multiply both sides by -1

f'(-x)=f'(x)

Therefore, f' is even

A good link for the chain rule is
http://www.sosmath.com/calculus/diff/der04/der04.html

The next scribe is Kyle.