1. Do Now Find the derivative of each 1) (use product rule) 2)
3.7 Chain Rule Tues Nov 4
Do Now
Find the derivative of each
1) (use product rule) 2)

2. HW Review p.167 #5-31 43 5) 23) 7) 2sin x cos x 25) y = 1
5) 23)
7) 2sin x cos x 25) y = 1
9) ) y = x + 3
11) )
13)
15) 31)
17) 43) -sinx, -cosx, sinx, cosx,
19) -sinx
21) f^8(x) = cosx f^37(x) = -sinx

3. Chain Rule Thm- If f and g are differentiable,
In words, the theorem says “the derivative of the outside times the derivative of the inside”

4. Examples of “Inside” A whole expression being raised to a power
An expression inside of a trig function
An expression inside of an exponent

5. Chain Rule cont’d
Another way to think of the chain rule is to use U-substitution
We let u = whatever is inside the parenthesis, then differentiate.

6. Ex 7.1
Differentiate

7. Ex 7.2
Find

8. Ex 7.3
Suppose the position of a weight hanging from a spring is given by
Find the velocity of the weight at any time t

9. Chain Rule and Trig
Compute the derivatives of

10. Closure
Journal Entry: When do we use the chain rule? What is the chain rule?
HW: p.175 #11-21, odds

11. 3.7 Multiple Chain Rule Wed Nov 5
Do Now
Use chain rule to differentiate: 1) 2)

12. HW Review p.175 #
11)
13)
15)
17)
19)
21)
29)
31)
33)
35)

13. HW Review
37)
39)
41)

14. Multiple Chain Rules
The more complicated a function gets, the more we will use the chain rule to differentiate
Set up the derivative before differentiating!

15. Ex
Differentiate

16. Ex 7.6
Find the derivative of

17. Ex 7.7
Find the derivative of

18. Practice:
Bookwork: p.175 #43-69 odds

19. Closure Hand in: Find the derivative of:
HW: p.175 #43-67 odds skip 57 59

20. 3-7 Chain Rule Practice Mon Nov 10
Do Now
Use chain rule to find each derivative 1) 2)

21. HW Review p.175 #43-69
43)
45)
47)
49)
51)
53)
55)
61)

22.
63)
65)
67)

23. Practice
(blue book) Worksheet p.214 #7-23, 31, 32, 35 skip 13, 21 22

24. Closure Hand in: Find the derivative of:
HW: worksheet p.214 #7-26, 31, 32, 35

25. 3.7 Chain Rule Practice Day 2 Tues Nov 11
Do Now
Use the chain rule to find dy/dx 1) 2)

26. HW Review worksheet 214 7) 37(x^3+2x)^36 (3x^2+2)
9) -2(x^3-7x^-1)^-3 (3x^2 +7x^-2)
10) -9(x^5-x+1)^-10 (5x^4-1)
11) -12 (3x^2-2x+1)^-4 (6x-2)
12) ½ (x^3-2x+5)^-1/2 (3x^2-2)
14) ¼ x^-3/4

27. 15) cos(1/x^2) (-2x^-3)
16) sec^2(x^1/2) (1/2 x^-1/2)
17) 20(cosx)^4 (-sinx)
18) (sinx)^3 (cosx)
19) 2(cos3x^1/2) (-sin3x^1/2) (3/2x^-1/2)
20) 4(tanx^3)^3 (sec^2x^3) (3x^2)
23) ½(cos5x)^-1/2 (-sin5x) (5)
31) –sincosx (-sinx)
32) costan3x (sec^2 3x) (3)
35) product rule

28. More Practice
(green book) worksheet p.219 #9-28

29. Closure
Journal Entry: If you had to describe how to use the chain rule to your friend, how would you?
HW: Finish worksheet