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Homework Help: A simple derivative that I can't get for the life of me

  1. Oct 16, 2012 #1
    Trying to get the 2nd derivative of this expression:

    ps/(1-qs) where p,q are constants and s is the variable. The solution is 2pq2(1-qs)3

    for the life of me I can't get that solution. every time I do it I get 2q/(1-q)2

    maybe I should mention that I'm using a probability generating function and trying to get the 2nd moment for the geometric distribution. But that shouldn't have an effect on the simple fact of the 2nd derivative.
  2. jcsd
  3. Oct 16, 2012 #2


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    Make sure you use the product or quotient rule and apply the chain rule properly.
  4. Oct 16, 2012 #3
    I've been doing that.
  5. Oct 16, 2012 #4


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    Shouldn't your answer at least depend on s? That said, I don't get the answer you show as a solution either.
  6. Oct 16, 2012 #5


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    How did you loose the "s" from the denominator? Show your work in detail.

  7. Oct 17, 2012 #6
    I didn't get that answer either that you show as a solution.

    I got qp+q^2ps/(1-qs)^3
  8. Oct 17, 2012 #7
    whenever i have a problem like this, i like to move my constants out front and rewrite things in fractions as negative exponents. in your case, i would rewrite the function as

    ps/(1-qs)=p*(s)(1-qs)^-1. then, ignore the p for now, since you can just multiply it out, and focus on find the derivative of s*(1-qs)^-1. should be pretty easy from there out. if i want to be more explicit, i write things out in function notation first, apply the chain rule/product rule (as i would here) with f(s),g(s), etc, and then plug in f(s),f'(s), etc, after i've figured out the proper form.
  9. Oct 17, 2012 #8
    ...which is also incorrect. :wink:
  10. Oct 17, 2012 #9
    Is it, I did the problem while sleeping, why don't you post a solution oay?
  11. Oct 17, 2012 #10
    I could post the solution, but it's not the done thing. People asking the questions should show their work so far. The OP hasn't yet.
  12. Oct 17, 2012 #11
    the reason the "s" disappears from the solution is because it is a PGF from statistics so after you differentiate you let s = 1 and obtain your solution.
  13. Oct 17, 2012 #12


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    "But that shouldn't have an effect on the simple fact of the 2nd derivative." You said you were just trying to find the second derivative. So why is there an s in the given solution?
  14. Oct 17, 2012 #13
    Ok, so you haven't asked for the 2nd derivative at all, then. Make your mind up.
  15. Oct 17, 2012 #14
    Are you suggesting yours is correct?
  16. Oct 17, 2012 #15
    No buddy i said i was falling asleep, so i am going to do the problem again now and i don't know if this boy here is talking about statistics and i don't know if i am right, i never know if i am right, but this here is what i get,

    D^2y/(dx)^2= 8pq^3/(1-qs)^5

    oh i took the second derivative of the second derivative that was given in the problem.

    So it would be the 4th derivative of the solution given in the initial problem, which was said to be wrong for that problem, so this is just the second derivative of that proposed solution then, eh.
  17. Oct 17, 2012 #16
    Fine. No problem, try again tomorrow.
    Last edited: Oct 17, 2012
  18. Oct 17, 2012 #17

    Ray Vickson

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    You say "I can't get that solution". I should hope not: the correct solution is
    2pq/(1-qs)^3. Can you get that?

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