AP Calculus BCWednesday, 30 September 2015

• OBJECTIVE TSW review for Friday’s test covering differentiation.

• ASSIGNMENTS DUE FRIDAY– WS Implicit Differentiation– WS Differentiation

Textbook Answers: Sec. 3.83

3 5) a) 1b)

x

y

72

1) a) b)y

20 20

cos9) a) b)

y

1 1

si11) a

n) b)

y

1 cos13)

cos 1

y xy

x xy

11

15in

) s y

331)

1

4y

2 2

3

2 432)

y x

y

3si

33) n

cos 1

y

y

6 2 4

73

3 34)

x x y

y

3

sin 4cos 636)

x x x xy

x

45) 14

47) 2413

49) 5

WS Product, Quotient, Chain Rules

1) 2 2) 2 ) 31825

4) 14 5) 350 ) 64

343

7) 2 8) 7e 9) e

10) 2

13) 1

16) 4 17) 6

14) 74

11) 4 12) 54

15) 1

18) 2

WS Product, Quotient, Chain Rules

WS Implicit Differentiation

2

1 2

)3d

dx yy

x x) 2

dydx

xy

2

2

2

2 3)

xx

yd x

y

y

dc4) ot c t o

dyx

dxy

25 tan )dydx

y 2 1 1cos c) 6 ot

dyydx

yy

WS Implicit Differentiation

3

2

2

21

16

7)34

dydx

d y

dx

y

y

x

2

2

5

2

2

2

8)dydx

d y

dx

y

x

y

x

2 2

2 2

39)

3

6

dydx

x

x y y

y

y x

3 2

2 3

25 4 4

4 4 25

91 3

13

0 1 )x x xy

x y y y

y

dy

x

dx

WS Differentiation

4 3

4) 1

4g x

x

265) 2 3f x x x

4

156) 2 sin

8y x

x

1 3 2 32 13

7) 3

f t t t

2

28)

2 7 2

2 7

x xh x

x

2

29)

2 2

1

t tg t

t

6 4 242 40 63 2810) f x x x x

3 sec11) an t 4y x x x x

12

1 131

3 1)

8 y x

2

2)

21

xf x

x

2) 26

a vertical tangent 3 @ 2) x

AP Calculus BC Derivatives Test Topics

Find a derivative using the definition. Find a derivative using the alternate

definition. Know when/where vertical tangents and cusps

exist. Use the derivative rules (shortcuts) to find

first and second derivatives. Product Rule Quotient Rule Chain Rule General Power Rule

Be able to discuss the relationship between continuity and differentiability.

Know the derivatives of the six trigonometric functions.

Applications. Find the slope of a tangent. Find the equation of a tangent line. Find points of horizontal and vertical

tangency.

AP Calculus BC Derivatives Test Topics

Use implicit differenitiation. First and second derivatives.

AP Calculus BC Derivatives Test Topics

The test is part with calculator, part without. Once you finish the “with” part, the calculator must

be put away for the rest of the test.

Study notes, PowerPoints, assignments, WS’s, and quizzes.

Wear a (PURPLE) JVHS shirt. No, I don’t know when the shirts will come in.

QUESTIONS???

AP Calculus BC Derivatives Test Topics