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First and Second Derivatives

  1. Mar 8, 2012 #1
    1. The problem statement, all variables and given/known data
    f(x)=X^2/(x^2-16)

    f(x)=1+x/1-X

    f(x)=X^3(X-2)^2

    Ive done the first and second derivatives but they just dont seem right

    2. Relevant equations
    Quotient/Chain/Product Rule


    3. The attempt at a solution
    f(x)=X^2/(x^2-16)
    (X^2-16)(2X)-(X^2)(2X)/(X^2-16)^2
    f'(x)=-32X^2/(X^2-16)^2
    (X^4-32X^2+256)(-64X)-(-32X^2)(4X^3-64X)/(X^4-32X^2+256)^2
    -64x^5+2048X^3-16384X+128X^5-2048X^3
    f''(x)=64X^5-16384X/(X^4-32X^2+256)^2

    f(x)=1+x/1-X
    (1-X)(1)-(1+X)(-1)/(1-X)^2
    f'(x)=2-2X/(1-X)^2
    (X^2-2X+1)(-2)-(2X-2)(2-2X)/(X^2-2X+1)^2
    f''(x)=2X^2+4X+2/(X^2-2X+1)^2

    f(x)=X^3(X-2)^2
    (X^3)(2X-4)+(3X^2)(X-2)^2
    2X^4-4X^3+3X^4-12X^3+12X^2
    f'(x)=5X^4-16X^3+12X^2
    5X^4-16^3+12X^2
    f''(x)=20X^3-48X^2+24X
     
  2. jcsd
  3. Mar 9, 2012 #2

    tiny-tim

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    hi mmajames! :smile:

    eugh! :yuck: this is impossible to read! :redface:

    try using the X2 button just above the Reply box (and a few more spaces) :wink:
     
  4. Mar 9, 2012 #3

    HallsofIvy

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    1. Are these three different functions??

    2. Please use parentheses 1+ x/x+ 3 is not the same as (1+ x)/(x+ 3).
     
  5. Mar 9, 2012 #4
    f(x)=X2/(x2-16)
    (X2-16)(2X)-(X2)(2X)/(X2-16)2
    f'(x)=-32X2/(X-16)2
    (X4-32X4+256)(-64X)-(-32X2)(4X3-64X)/(X4-32X2+256)2
    -64x^5+2048X^3-16384X+128X5-2048X3
    f''(x)=64X5-16384X/(X4-32X^2+256)2

    f(x)=(1+x)/(1-X)
    (1-X)(1)-(1+X)(-1)/(1-X)2
    f'(x)=2-2X/(1-X)2
    (-2X+1)(-2)-(2X-2)(2-2X)/(X2-2X+1)2
    f''(x)=2X2+4X+2/(X2-2X+1)22

    f(x)=X3(X-2)2
    (X3)(2X-4)+(3X2)(X-2)2
    2X4-4X3+3X4-12X3+12X2
    f'(x)=5X4-16X3+12X2
    5X^4-163+12X2
    f''(x)=20X3-48X2+24X



    And yes Three different functions
     
  6. Mar 10, 2012 #5

    tiny-tim

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    hmm … i can see two mistakes already :redface:

    sorry, but i'm not checking the rest until you've gone over them again, to find any other mistakes

    also, (as HallsofIvy :smile: says) please use more brackets
     
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