Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57

Calculus One

Derivatives of Trig Functions

IF: THEN:

F(x) = sin x F'(x) = cos x

F(x) = cos x F'(x) = - sin x

F(x) = tan x F'(x) = sec2 x

F(x) = cot x F'(x) = - csc2 x

F(x) = sec x F'(x) = sec x tan x

F(x) = csc x F'(x) = - csc x cot x

These formulas can be used in conjunctions with other derivative rules such as the constant multiple rule,

product and quotient rules, the chain rule. Use these formulas to determine the derivative of the

following functions.

1. sin (8x) 2. cos (5x) 3. tan (3x) 4. csc (7x)

5. sin2(x) 6. cos

3(x) 7. cos

3(5x) 8. cot

5 (

3

2x)

9. cot4 (3x) 10. csc

3(x

2 – 3)

.

Trigonometric expressions are often combined with algebraic expressions, and can often be simplified

before and/or after calculating the derivative using trigonometric substitutions. Determine the derivatives

of the following functions, and simplify your results.

11. f(x) = 3cotx - 2

x

12. f(x) = cos

sin

x

x

– 3cot(2x)

13. f(x) = 2sinx + x2 – π tanx 14. f(x) =

cos x

x

15. f(x) = 2 1

3

( cos )

sin

− x

x

16. f(t) = t2csc t

17. f(x) = cos(3x)sin(2x)

Homework: Page 115: 19, 21, 23, 51 Page 126: odds 39 – 53 Page 137: odds 41 - 57