Wetzel

Math 140

2.4 – The Chain Rule

The Chain Rule –

                                       where  has two or more terms

Ex.:  Find

1.)                                                     2.) 

3.)                                                     

More Trig. Derivatives -       (*MEMORIZE*)

4.)                                                          5.) 

Average Rate of Change –                 =   

            Derivative – the instantaneous rate of change at a point

            Average rate of change – the average rate of change between two points

Ex:

6.)  If a free-falling object is dropped from a height of 100 feet and air resistance is neglected, the height h (in feet) of the object at time t (in seconds) is given by

Find the average velocity of the object over the following intervals.

            a.)  [1,2}                                                          b.) [1,1.5]

7.)  The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model

where t is the time in seconds.  Approximate the average volume of air in the lungs during one cycle.

HW:  p.137 #7-29odd, 41-49odd