## (Solved) Math 2211 3.5 Review Name________________________ Just Relax and Think Positively! I Know you CAN Do This! Differentiate: f(x) = 30 3 2. F(x) = 4 8...

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Math 2211 3.1âˆ’3.5 Review Name________________________ Just Relax and Think Positively!!!! I Know you CAN Do This!!!
Differentiate:
1. f(x) = âˆš30
3 2. F(x) = 4 8
3. f(t) = 1 6 âˆ’ 3 4 + 2 4. h(x) = (x âˆ’ 2)(2x + 3)
5. B(y) = cy âˆ’6
7 6. h(x) = âˆš 7 + âˆš 2
7. y = âˆš(x â€“ 1)
8. f(x) = 2 âˆ’3+1
2
1 2 9. y = (âˆš + 3 ) âˆš 10. y = ex + 1 + 1
11. g(x) = âˆš 12. y = 1+
+1 13. y = 3+âˆ’2 14. y = (âˆ’1)2
15. y = 2cscx + 5cosx
16. f(x) = âˆš sin x
17. G(x) = ex(tanx âˆ’ x) 18. y = 1+sin +cos 19. f(t) =
20. y = cot 1âˆ’sec tan 21. y = x3âˆš 2 + 5
22. F(x) = (4x â€“ x2)100
23. f(x) = (1 + x4)2/3
3 24. f(t) = âˆš1 + tan 1 2 25. y = ( 3 âˆ’ 5) (3 3 + 5 2 âˆ’ 7)
26. y = sin((3 2 + 2 + 3)4 )
27. y = 5sinâˆš âˆ’ 3
28. y = 6 (4 3 âˆ’ 7 + 5)
29. y = eâˆ’2t cos 4t
30. h(t) = (t4 âˆ’ 1)3 (t3 + 1)4
31. y = 101âˆ’ 2 2 5 32. G(y) = (+1) 33. f(t) = âˆš 2 +4 34. y = esec 3x
35. y = 2xâˆš 2 + 1
36. Find an equation of the tangent line to the curve y = x4 + 2x2 âˆ’ x at the point (1, 2).
37. Find an equation of the normal line to the curve y = (1 + 2x)2 at the point (1, 9).
38. Find an equation of the tangent line to the curve y = x âˆ’ âˆš at the point (1, 0).
39. Find an equation of the tangent and normal lines to the curve y = (2 + x)eâˆ’x at the point (0, 2).
3 40. Find the first and second derivatives of the function G( r) = âˆš + âˆš . 41. The equation of motion of a particle is s = t4 âˆ’ 2t3 + t2 â€“ t, where s is in meters and t is in seconds.
a. Find the velocity and acceleration as functions of t.
b. Find the acceleration after 1 second.
42. For what values of x does the graph of f(x) = x3 + 3x2 + x + 3 have a horizontal tangent?
43. Find an equation of the tangent line to the curve y = (1 + 2x)10 at the point (0, 1).
44. Find an equation of the tangent line to the curve y = âˆš1 + 3 at the point (2, 3). 45. Find f '(x) and f ''(x): f(x) = 2âˆ’1
46. Find f '(x) and f ''(x): f(x) = cos(x2)
47. Find f '(x) and f ''(x): f(x) = cos2x
48. Find f '(x) and f ''(x): f(x) = Find dy/dx by implicit differentiation:
49. 2âˆš + âˆš = 3
50. 2x3 + x2y âˆ’ xy3 = 2
51. y5 + x2y3 = 1 + y 2 52. Use implicit differentiation to find an equation of the tangent line to the curve
x2 + 2xy â€“ y2 + x = 2 at the point (1, 2) Math 2211 1. 0 2. 6x7
3. 3t5 âˆ’12t3 +1
4. 4x âˆ’ 1
5. âˆ’6cyâˆ’7
6.
7. 7
2
3
2 2 5â„2 + 7 âˆ’5â„7
1 1â„2 âˆ’ 2 âˆ’1â„2 8. 3xâˆ’2 âˆ’ 2xâˆ’3
1 2 9. 1 + 3 âˆ’5â„6 âˆ’ 3 âˆ’5â„3
10. ex+1
1 11. 1â„2 + ( âˆ’1â„2 )
2 12.
13.
14. (+1)2
âˆ’2 3 âˆ’3 2 âˆ’3
( 3 + âˆ’2)2
âˆ’âˆ’1
( âˆ’ 1)3 15. âˆ’2cscxcotx âˆ’ 5sinx
16. âˆšcosx + 2âˆš 17. ( 2 âˆ’ 1 + âˆ’ )
18. (+)2 19. âˆ’ 2 + 3.1-3.5 Review SOLUTIONS 20. (1âˆ’)
2 21. 4 ( 2 + 5)âˆ’1â„2 + 3 2 ( 2 + 5)1â„2
22. 100(4x âˆ’ x2)99 (4 âˆ’ 2x)
23.
24. 8 3
3 3 âˆš1+ 4 2 3 3 âˆš(1+)2 25. âˆ’70 âˆ’6 + 51 âˆ’4 + 12 âˆ’3 âˆ’ 5 âˆ’2
26. cos(3 2 + 2 + 3)4 [4(3 2 + 2 + 3)3 (6 + 2)]
27. 5âˆšâˆ’3
2âˆšâˆ’3 28. 6(12 2 âˆ’ 7) [tan(4 3 âˆ’ 7 + 5)]5 2 (4 3 âˆ’ 7 + 5)
29. âˆ’2 âˆ’2 (24 + 4)
30. 12 2 ( 4 âˆ’ 1)2 ( 3 + 1)3 (2 4 + âˆ’ 1)
31. âˆ’2x(ln10)101âˆ’
32.
33. 2 5 9 (+2)
(+1)6
4 âˆ’ 2
2 1â„2 ( 2 +4)3â„2 34. 3 3 33
35. 2(2 2 +1)
âˆš 2 +1 36. y = 7x 5
37. y = âˆ’ 1
12 x+ 1 1 2 2 38. y = âˆ’ 109
12 39. Equation of the tangent line: y = âˆ’x + 2; Equation of the normal line: y = x + 2.
1 1 40. G1(r) = 2 âˆ’1â„2 + 3 âˆ’2â„3; 1 G11(r) = âˆ’ 4 âˆ’3â„2 âˆ’ 41. a v(t) = 4t3 âˆ’ 6t2 +2t âˆ’ 1; a(t) = 12t2 âˆ’ 12t + 2
1 42. âˆ’1 Â± âˆš6
3 2 âˆ’5â„3 9 b. a(1) = 2m/s2 43. y = 20x + 1
44. y = 2x â€“ 1
45. f1(x) = âˆ’ 2 âˆ’1
( 2 âˆ’1)2 ; ; â€()= 2 3 +6
( 2 âˆ’1)3 46. y'= âˆ’2xsin(x2); y'' = âˆ’4x2cos(x2) âˆ’ 2 sin(x2) 47. y' = âˆ’2cosxsinx; y'' = âˆ’2cos2x + 2sin2x 48. y'= âˆ™ ;
49. â€“
50. 2âˆš
âˆš âˆ’6 2 âˆ’2+ 3 2 âˆ’3 2
2 51. 2( âˆ’ 2 )
5 4 +3 2 2 âˆ’ 7 3 2 2 52. y = âˆ’ y''= âˆ™ + âˆ™ âˆ™ 2

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