Solve questions 8, 20, 32

6.6 EXERCISES 1-10 Find the exact value of each expression. 22-35 Find the derivative of the functic 1. (a) sin '(0.5) (b) cos ' (-1) possible. 2. (a) tan ' 3 (b) sec 1 2 22. y = tan '(x2) 3. (a) csc V2 (b) cos '(3/2) 23. y = (tan 'x)2 24. 4. (a) cot (-3) (b) arcsin 1 25. y = sin '(2x + 1) 26 5. (a) tan(arctan 10) (b) arcsin (sin(517/4)) 27. y = x sin 'x + VI - x2 28 6. (a) tan (tan 37/4) (b) cos(arcsin ?) 29. F(x) = x sec '(x]) 30. 7. tan( sin '(3)) 8. csc(arccos ) 31. y = arctan(cos #) 9. cos(2 sin (13)) 10. cos( tan ' 2 + tan ' 3) 32. y = tan (x - VI + x2) 11. Prove that cos(sin x) = V1 -x2 33. h(t) = cot '(t) + cot '(1/1) 12-14 Simplify the expression. 34. y - tan 12. tan(sin x) 13. sin(tan 'x) 14. sin (2 arccos x) 35. y = arccos b + a cos x Os A 15-16 Graph the given functions on the same screen. How are a + bcos x these graphs related? 15. y = sin x, -7/2 5 x 7/2; y = sin x; ly 36-37 Find the derivative of the functic 16. y - tan x, 7/2 the function and its derivative. 36. f(x) = arcsin(e*) 37 17. Prove Formula 6 for the derivative of cos _ by the same method as for Formula 3. 38. Find y' if tan "'(x2y) = x + xy?. 18. (a) Prove that sin x + cos 'x = T/2. (b) Use part (a) to prove Formula 6. 39. If g(x) = x sin '(x/4) + 16 - x 19. Prove that (cot x) = d 40. Find an equation of the tangent line dx 1 + x2 y = 3 arccos(x/2) at the point (1, T 20. Prove that - (sec 'x) = 41-42 Find f'(x). Check that your ans xVx2 - 1 comparing the graphs of f and f'. 21. Prove that- d dx (csc x) = 41. f(x) = V1 - x2 arcsin x 42. x x2 - 1