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Find second derivitive

  1. May 30, 2012 #1
    Find second derivitive!!

    1. The problem statement, all variables and given/known data
    f(x)=4(x^2-2)^3


    2. Relevant equations
    Chain rule??


    3. The attempt at a solution
    f'=12(x^2-2)^2(2x)
    =24x(x^2-2)^2

    f''=2(24x)(x^2-2)(2x)
    96x^2(x^2-2)
    After this, I got lost...
     
  2. jcsd
  3. May 30, 2012 #2
    Re: Find second derivitive!!

    Looks good to me.
     
  4. May 30, 2012 #3
    Re: Find second derivitive!!

    Really? I even went further & distributed and got: 96x^4-192x^2 ... & still got it wrong!
     
  5. May 30, 2012 #4

    Dick

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    Re: Find second derivitive!!

    You'll need to use the product rule when you go from f' to f''. f' is a product of the two functions (24x) and (x^2-2)^2.
     
  6. May 30, 2012 #5
    Re: Find second derivitive!!

    Ok.. so would I set it up like this>> (24)[2(x^2-2)]+(x^2-2)^2(24) ??
     
  7. May 30, 2012 #6

    Dick

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    Re: Find second derivitive!!

    No. That's not right. Review how the product rule works and try it again.
     
  8. May 30, 2012 #7

    HallsofIvy

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    Re: Find second derivitive!!

    No, that is also wrong. Please show exactly how you are trying to do this.
     
  9. May 30, 2012 #8
    Re: Find second derivitive!!

    Product rule: d/dx[fs]=fs'+sf'
    24x×2(x^2-2)+(x^2-2)^2×24
    Is that the right way?
     
  10. May 30, 2012 #9

    Mark44

    Staff: Mentor

    Re: Find second derivitive!!

    No, that isn't right either. You also have to use the chain rule when you differentiate (x2 - 2)2.

    It's NOT a good idea to use x for multiplication, especially when x is the variable. You've made it slightly easier by bolding some of the variables. In calculus, we generally don't use x for multiplication.
     
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