3.7 Chain RuleTues Nov 4

Do Now

Find the derivative of each

1) (use product rule)

2)

HW Review p.167 #5-31 43

• 5) 23)

• 7) 2sin x cos x 25) y = 1

• 9) 27) y = x + 3

• 11) 29)

• 13)

• 15) 31)

• 17) 43) -sinx, -cosx, sinx, cosx,

• 19) -sinx

• 21) f^8(x) = cosx f^37(x) = -sinx

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”

Examples of “Inside”

• A whole expression being raised to a power

• An expression inside of a trig function

• An expression inside of an exponent

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.

Ex 7.1

• Differentiate

Ex 7.2

• Find

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

Chain Rule and Trig

• Compute the derivatives of

Closure

• Journal Entry: When do we use the chain rule? What is the chain rule?

• HW: p.175 #11-21, 29-41 odds

3.7 Multiple Chain RuleWed Nov 5

• Do Now

• Use chain rule to differentiate:

• 1)

• 2)

HW Review p.175 #11-21 29-41• 11) • 13)• 15)• 17) • 19)• 21)• 29)• 31)• 33)• 35)

HW Review • 37)

• 39)

• 41)

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!

Ex

• Differentiate

Ex 7.6

• Find the derivative of

Ex 7.7

• Find the derivative of

Practice:

• Bookwork: p.175 #43-69 odds

Closure

• Hand in: Find the derivative of:

• HW: p.175 #43-67 odds skip 57 59

3-7 Chain RulePractice

Mon Nov 10• Do Now

• Use chain rule to find each derivative

• 1)

• 2)

HW Review p.175 #43-69• 43)

• 45)

• 47)

• 49)

• 51)

• 53)

• 55)

• 61)

63 65 67

• 63)

• 65)

• 67)

Practice

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

Closure

• Hand in: Find the derivative of:

• HW: worksheet p.214 #7-26, 31, 32, 35

3.7 Chain Rule Practice Day 2Tues Nov 11

• Do Now

• Use the chain rule to find dy/dx

• 1)

•

• 2)

HW Review worksheet 214

• 7) 37(x^3+2x)^36 (3x^2+2)

• 8) 6(3x^2+2x-1)^5 (6x+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

• 15) cos(1/x^2) (-2x^-3)• 16) sec^2(x^1/2) (1/2 x^-1/2)• 17) 20(cosx)^4 (-sinx)• 18) 4 + 20(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

More Practice

• (green book) worksheet p.219 #9-28

Closure

• Journal Entry: If you had to describe how to use the chain rule to your friend, how would you?

• HW: Finish worksheet