This document discusses the chain rule for taking derivatives of composite functions. It explains that when differentiating a function composed of an outer and inner function, the derivative is the product of the derivative of the outer function and the derivative of the inner function. It provides examples of applying the chain rule to functions with multiple compositions.

1. 1

2. e
y w
da
learn To
ed ab
out
le!
Ru
in
a
ch
he
t
2

3. It states:
3

4. It basically tells
you how to get
the derivative of
a function that is
composed of other
functions.
4

5. Seems simple enough...
5

6. Well let's try it out
6

7. 7

8. Let's break it up
into its functions
8

9. 9

10. Outer
function
Inner function
10

11. Outer
function
Inner function
Our rule:
11

12. Outer
function
Inner function
Our rule:
let's look at this part
12

13. Outer
function
Inner function
Our rule:
Now let's look at just this
13

14. Outer
function
Inner function
We Know how to
work with this
14

15. Outer
function
Inner function
Remember:
is fed
So
15

16. Outer
function
Inner function
Remember:
16

17. Outer
function
Inner function
Our rule:
17

18. Outer
function
Inner function
Our rule:
Now let's look at just this
18

19. Outer
function
Inner function
19

20. 20

21. Or just look at it using power law, a tad bit
more complicated but for some reason this
is the first that comes to my mind when I
look at these (guess I'm just odd)
21

22. Outer
function
Inner function
22

23. Outer
function
Inner function
Now let's put it all
together
23

24. Outer
function
Inner function
together
Now let's put it all
24

25. Outer
function
Inner function
25

26. This will barely ever
appear on a test as an
answer to multiple
choice
26

27. This might. The 7 has been
factored in and it is no
longer color coordinated.
27

28. Well that
wasn't that
hard
28

29. Now a bunch more
a lot faster
29

30. 30

31. 31

32. Now we run into a
slightly different case
32

33. 3 functions !
33

34. 34

35. So what do we do?
35

36. We use chain
rule more than
once!
36

37. From what I saw this is
what I think using chain
rule more than once is:
37

38. Following the pattern
for four functions:
I think this is right
38

39. Back to this then
39

40. 40

41. 41

42. 42

43. And from here it is just grant work
43