Chapter 3.02
Remember that you should be graphing each function and its derivative, and
visually checking that the derivative graph makes sense, for the reasons
listed in the Chapter 3.01 homework.

1
2
3
4
5 (when you graph it, set your x window to [-1, 5] )
6
7 WEP

9
16 WEP
18 WEP
22 WEP
23
26 WEP
27
28
29 WEP
30 WEP
31 WEP
32 WEP
36

41
42

57
58 WEP
59 MTH/MTHT
60 MTH/MTHT
61 MTH/MTHT

QA: find the derivative of these. Remember to graph each function and its
derivative.
i) 1/(1+exp(x))
ii) exp(x) / (1+exp(x) )
iii) 1 - 1/(1+exp(x))   [note this is not the same as (1-1)/(1+exp(x)) ]
iv) 1/(1+x^2)

QB: You might be wondering: why do the product and quotient rules look so
different from
each other?  An article I read gave more similar-looking forms:
(fg)' =    fg  (f'/f + g'/g)
(f/g)' = (f/g) (f'/f - g'/g)
(College Math Journal 42:4 September 2011 page 323, by Roger Eggleton and
Vladimir Kustov; it also gives rules for 3 functions at a time, and second
derivatives)

i) Do a little algebra to show that these indeed are equivalent to the rules
we learned in the book.
ii) What is the mathematical downside to using the product rule in this new
form?
iii) Let's think of a useful, natural interpretation for f'/f or g'/g: if
f(5)=100 and f'(5)=3,
then f is increasing at 3% per unit time, right? How is this related to f'/f ?