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Maclaurin Polynomial

  1. Dec 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Compute the sixth derivative of f(x)=sin(x^2) at x=0. Hint: Maclaurin polynomial may be helpful to you.

    2. Relevant equations
    The taylor expansion/maclaurin expansion for sin.

    3. The attempt at a solution
  2. jcsd
  3. Dec 15, 2008 #2


    Staff: Mentor

    Hint: Maclaurin polynomial may be helpful to you.
    Do you know the Maclaurin series for sin(x)?
  4. Dec 15, 2008 #3
    yes but how does the x^2 alter the expansion?
  5. Dec 15, 2008 #4


    Staff: Mentor

    Replace each occurrence of x in the Maclaurin series expansion for sin(x) with x^2.
  6. Dec 15, 2008 #5
    So the expansion would be:

    x^2-x^6/3!+x^10/5! ?
  7. Dec 15, 2008 #6


    Staff: Mentor

    That would be the first three nonzero terms, yes. Keep in mind there are quite a few terms whose coefficients are zero, so sin(x^2) = 0 + 0x + x^2 + 0x^3 + 0x^4 + 0x^5 - x^6/3! + ...

    Regarding your original problem, keep in mind the general formula for the Maclaurin series, and how you get the coefficients of the various powers of x.
  8. Dec 15, 2008 #7
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