Exercises

1. Find the derivatives of the following functions three different ways using Maple. From the definition, using the D command, and using the diff command. Note that Maple has its own ideas of what form the answer should take, so some of your answers may look unfamiliar or be more complicated than you think they should.

   1. 

   2. 

   3. 

   4. 

   5. 

2. Determine the derivative of the function f(x) defined by

   

   for all values of x for which f'(x) exists. Describe how you obtained your results.

3. Suppose that s(t), defined as

   

   for , describes motion of a particle in one dimension. That is, s is the distance of the particle from some reference point as a function of time.

   1. Find the secant line of the graph of s between t=1 and t=2.
   2. Describe how you can use your answer to the first part of this exercise to compute the average velocity of the particle over the time interval . Report the value of the average velocity.