Scribe Post Thursday October 14, 2010

Today we started off class by going over a few problems from assignment 4. Mr. O'Brien then briefly talked about what may be on the quiz tomorrow. He told us everything on assignments 1-5 is fair game for the quiz. There are several things from this unit he suggested that we commit to memory, which are stated below.


Things To Remember:

2 derivative definitions:






For the Derivative of a Constant





product rule:






quotient rule:







trig derivatives
http://archives.math.utk.edu/visual.calculus/2/trig.1/

memorized values from pre-calc
http://www.sosmath.com/trig/Trig2/trig2/trig2.html



Our focus during this class was the chain rule:

The Chain rule can be defined as:



Or it can be defined using words as:
"The derivative of a composition of two functions is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the outer function."

Some of the examples we did in class are shown below:










UPDATE:
The chain rule is a crucial concept to understand as we move along in Calculus. It will come up constantly in many of the things we do from now on. For example implicit differentiation can not be done without the chain rule. To see how the chain rule is used in implicit differentiation, take a look at Kyles post: http://apcalcred1011.blogspot.com/2010/10/scribe-post-tuesday-october-19-2010.html

This website http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html shows several chain rule problems with detailed solutions to each, which may be helpful. This website http://archives.math.utk.edu/visual.calculus/2/chain_rule.4/index.html has some interactive chain rule problems that also might be helpful. And if you have access to youtube, I found this video to be helpful: http://www.youtube.com/watch?v=6kScLENCXLg

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