AP Derivatives

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AP Derivatives

  1. 1. Derivative?f(x)= sinx
  2. 2. Answerf(x)= cosx
  3. 3. Derivative?xxf1)( =
  4. 4. Answer21)(xxf −=
  5. 5. What does this mean??lim0=−+→ hee xhxh
  6. 6. Answer:It is asking for thederivative of ex. Thenotation is the limitdefinition of the derivative(difference quotient)
  7. 7. Derivative?)()(xgxfy =
  8. 8. Answer-Quotient Rule( )LowLowHighDLowLowDHighyxgxgxfxfxgy−=−=)()()()()( 2
  9. 9. Derivative?f(x)= ax
  10. 10. Answeraaxf xln)( =
  11. 11. Derivative?f(x)= cotx
  12. 12. Answerf(x)= -csc2x
  13. 13. Derivative?f(x)= secx
  14. 14. Answerf(x)= secxtanx
  15. 15. Derivative?f(x)= arctanx= tan-1x
  16. 16. Answer211)(xxf+=
  17. 17. Derivative?f(x)= cosx
  18. 18. Answerf(x)= -sinx
  19. 19. Derivative?f(x)= ex
  20. 20. Answerf(x)= ex
  21. 21. Derivative?f(x)= arccosx= cos-1x
  22. 22. Answer211)(xxf−−=
  23. 23. Derivative?f(x)= tanx
  24. 24. Answerf(x)= sec2x
  25. 25. Derivative?f(x)= arccscx= csc-1x
  26. 26. Answer1||1)(2−−=xxxf
  27. 27. Derivative?f(x)= lnx
  28. 28. Answerxxf1)( =
  29. 29. Derivative?f(x)= cscx
  30. 30. Answerf(x)= -cscxcotx
  31. 31. Derivative?y=f(x)g(x)
  32. 32. Answer-Product Ruley= f(x)g(x)+f(x)g(x)
  33. 33. Derivative?f(x)= arcsinx= sin-1x
  34. 34. Answer211)(xxf−=
  35. 35. Derivative?f(x)= arccotx= cot-1x
  36. 36. Answer211)(xxf+−=
  37. 37. Derivative?f(x)= arcsecx= sec-1x
  38. 38. Answer1||1)(2−=xxxf
  39. 39. Derivative?xxf alog)( =
  40. 40. Answeraxxfln1)( =
  41. 41. Derivative?y= f(g(x))
  42. 42. Answer-Chain Ruley= f(g(x))g(x)
  43. 43. dy=?
  44. 44. Answerdy=f’(x)dx
  45. 45. y=?
  46. 46. Answery=f(x+ x)-f(x)
  47. 47. Derivative of Inverse
  48. 48. Answer)(1)( 1yfxf −=

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