Derivative Rules

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Author:
jlim007
ID:
13453
Filename:
Derivative Rules
Updated:
2010-04-07 12:28:36
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Derivative Rules
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Description:
27 Derivative Rules
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  1. d/dx [cu] =
    cu'
  2. d/dx [u ± v] =
    u'± v'
  3. d/dx [uv]=
    uv' + vu'
  4. d/dx [u/v]=
    vu'-uv'/v²
  5. d/dx [c]=
    0
  6. d/dx [uⁿ]=
    nuⁿ⁻¹u'
  7. d/dx [x]=
    1
  8. d/dx [|u|]=
    u/|u|(u') , u≠0
  9. d/dx [ln u]=
    u'/u
  10. d/dx [eⁿ]=
    eⁿn'
  11. d/dx [log a u]=
    u'/ln(a)u
  12. d/dx [aⁿ]=
    (ln a)aⁿn'
  13. d/dx [sin u]=
    (cos u)u'
  14. d/dx [cos u]=
    -(sin u)u'
  15. d/dx [tan u]=
    (sec²u)u'
  16. d/dx [cot u]=
    -(csc²u)u'
  17. d/dx [sec u]=
    (sec u tan u)u'
  18. d/dx [csc u]=
    -(csc u cot u)u'
  19. d/dx [arcsin u]=
    u'/√1-u²
  20. d/dx [arccos u]=
    -u'/√1-u²
  21. d/dx [arctan u]=
    u'/1-u²
  22. d/dx [arccot u]=
    -u'/1-u²
  23. d/dx [arcsec u]=
    u'/|u|√u²-1
  24. d/dx [arccsc u]=
    -u'/|u|√u²-1
  25. cos (0) =
    1
  26. sin (0)=
    0
  27. e⁰=
    1

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