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Transcript 
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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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. cos3(x)
7. cos3(5x)
2
8. cot5 ( x)
3
9. cot4 (3x)
.
10. csc3(x2 – 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 x
– 3cot(2x)
sin x
13. f(x) = 2sinx + x2 – π tanx
15. f(x) =
2(1 − cos x )
3 sin x
14. f(x) =
cos 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
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