Derivatives of a Special Class of Functions

This lab has two goals.

a) Discover the general class of functions with which we are working.

b) Discover a general formula to calculate the derivative of a function from this class.

Find the derivatives of the following functions.

1.

2.

3.

4.

5) By observing what is going on above make a hypothesis for the derivative of the following:

Find derivatives for the following functions.

6.

7.

8.

9. Note: The MAPLE representation of is exp(x)

10. By observing the patterns above, make a hypothesis for the derivative of

11. Make a conjecture for the derivative of tan(g(x)).

12. Make a conjecture for the derivative of.

13. In a paragraph or two, summarize what you have learned from this lab. In particular, you have looked at the following types of functions:

.

Determine a more general class of functions these types fit under and make a hypothesis about the derivative for this class of functions. What assumptions are necessary for you hypothesis to be true?

14. (Optional)

Try to prove the derivative formula you have hypothesized for this special class of functions.

15. How would you generalize the derivative formula to differentiate a function of the form

F(x) = f(g(h(x)))?