Derivatives

Derivatives - Spring 2011 MATH 1550 - 19 p. 3 Calculate the...

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Derivatives Spring 2011 MATH 1550 - 19 p. 1 Name: Calculate the following derivatives 1. f ( x ) = e x sin x 2. f ( x ) = e x cos x 3. f ( x ) = x 2 tan x 4. f ( x ) = (1 + x ) 2 (sin x + x ) 5. f ( x ) = sin x x 6. f ( x ) = 1+cos x 1 - cos x 7. f ( x ) = x cot x 8. f ( x ) = sin 2 x + cos 2 x 9. f ( x ) = e - x sin x Find the second derivative for the following functions 10. f ( x ) = tan x 11. f ( x ) = cot x 12. f ( x ) = sec x 13. f ( x ) = csc x 14. f ( x ) = 4 sin x + 2 cos x 15. f ( x ) = e x sin x 16. f ( x ) = e x cos x
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Derivatives Spring 2011 MATH 1550 - 19 p. 2 Use the chain rule to calculate the following derivatives 17. f ( x ) = sin 4 x 18. f ( x ) = ( x 2 + 9) 4 19. f ( x ) = 3 cos 3 x 20. f ( x ) = 1 - x 4 21. f ( x ) = e (10 - x 2 ) 22. f ( x ) = tan 6 x 23. f ( x ) = ( x 2 - cos x ) 4 24. f ( x ) = sin(cos(sin x )) 25. f ( x ) = tan 3 x + tan( x 3 ) 26. f ( x ) = ( x + 1) 2 (2 x - 1) 3 27. f ( x ) = sin( x 2 ) cos( x 2 ) Calculate the following deriviatives implicitly 28. 3 xy = x 2 + y 2 - 4 x 29. x 2 4 - y 2 9 = 1 30. y 2 = x 3 - x 31. y 2 = 2 + xy 32. 2 x = 2 y 3 x - y 33. x 2 + y 2 = 25 xy 2 34. x sin y + y cos x = xy 35. e xy = x 2 + y 2
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Derivatives
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Unformatted text preview: Spring 2011 MATH 1550 - 19 p. 3 Calculate the following derivatives using whatever rules and facts you need 36. f ( x ) = ln(4 x-sin x ) 37. f ( x ) = x ln x 38. f ( x ) = x ln( x + e x ) 39. f ( x ) = (ln( x 2 )) 3 40. f ( x ) = ln(3 x ) sec(2 x + 1) 41. f ( x ) = 2 x x 2 42. f ( x ) = tan(ln(2 x )) 43. f ( x ) = e 2 x x 44. f ( x ) = x x 45. f ( x ) = 4 sin( x ) 46. f ( x ) = x 3-3 x + x-3 47. f ( x ) = tan-1 (ln( x )) 48. f ( x ) = (cos 7 x )(sin 4 x )( x 3-3 x + 1) 5 49. f ( x ) = (ln(6 x )-6 cot( x )) 5 50. f ( x ) = ln(csc( x 2 ))...
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Derivatives - Spring 2011 MATH 1550 - 19 p. 3 Calculate the...

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