Calculus

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Author:
lbwiggains
ID:
41646
Filename:
Calculus
Updated:
2010-10-18 16:30:33
Tags:
Stewart Calculus Differentiation Integration
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Description:
Review for rules of differentiation and integration, Stewart Textbook 5th ed.
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  1. Derivative of a constant
    d/dx(c)=
    zero
  2. The power rule
    d/dx(xn)=
    nxn-1
  3. d/dx[cf(x)]=
    c d/dx f(x)
  4. The sum rule: d/dx[f(x) + g(x)]=
    d/dx f(x) + d/dx g(x)
  5. The difference rule:
    d/dx[f(x)-g(x)]=
    d/dx f(x) - d/dx g(x)
  6. Product Rule:
    (f(x)g(x))'=
    fg ' + gf '. Or d/dx[f(x)g(x)]= f(x) d/dx g(x) + g(x) d/dx f(x)
  7. Quotient Rule:
    (f/g)'=
    (gf ' - fg ')/g2
  8. d/dx (sin x)=
    cos x
  9. d/dx (cos x)
    - sin x
  10. d/dx (tan x)
    sec2x
  11. d/dx (csc x)=
    -csc x cot x
  12. d/dx (sec x)=
    sec x tan x
  13. d/dx (cot x)=
    -csc2x
  14. Chain rule:
    If F(x)= f(g(x)), then F(x)' =
    F(x)'= f ' (g(x))g'(x). Derivative of the outer function * inner function * derivative of the inner function
  15. Power Rule Combined with the Chain rule:
    d/dx (un)=
    nun-1 du/dx

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