## Answers to ExercisesforSection 3: Derivatives of Trigonometric Functions

 2. The Six Trigonometric Functions 3. Derivatives of Trigonometric Functions 4. Integrals of Trigonometric Functions Trigonometric Functions Main Page "Real World" Page

1. f'(x) = cos x + sin x

3. g'(x) = (cos x)(tan x) + (sin x)(sec2x)

5. h'(x) = 2cosecx cotan x sec x tan x + 3

7. r'(x) = cos x x sin x + 2x

9. s'(x) = (2x1)tan x + (x2x+1)sec2x

 11. t'(x) = (cosec2x)(sec x)(tan x) sec x(1 + sec x) 2

13. k'(x) = 2cos x sin x

15. j'(x) = 2sec2x tan x

17. u'(x) = (2x 1)sin(x2 x)

19. v'(x) = (2.2x1.2+1.2)sec(x2.2+1.2x1)tan(x2.2+1.2x1)

21. w'(x) = sec x tan x tan(x2 1) + 2x sec x sec2(x2 1)

23. y'(x) = ex(sin(ex) + cos x sin x)

25. z'(x) = sec x

27. z'(x) = sec x

31.e2x[2sin(3x) + 3cos(3x)]

33. 1.5[sin(3x)] 0.5cos(3x)

35. sec(x3/x21) tan(x3/x21) (x43x2) / (x21)2

37. (1/x)cotan(2x1) 2ln |x| cosec2(2x1)

39. c'(t) = (3.5)(2)cos[2(t0.75)]; c'(0.75) \$21.99 per year 42¢ per week

41. (a) d(t) = 5cos(2t/13.5)+10 (b) d'(t) = (10/13.5)sin(2t/13.5); d'(7) 0.270. At noon, the tide was rising at a rate of 0.270 feet per hour.

43. c'(t) = 1.035t[ln |1.035|(0.8sin(2t) + 10.2) + 1.6 cos(2t)];

c'(1) = 1.035[10.2ln |1.035|+ 1.6] \$5.5656 per year, or \$0.11 per week.

 2. The Six Trigonometric Functions 3. Derivatives of Trigonometric Functions 4. Integrals of Trigonometric Functions Trigonometric Functions Main Page "Real World" Page