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Taylor Series Problem

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  1. Jan 11, 2015 #1
    1. The problem statement, all variables and given/known data

    Let f(x)=cos(x^5). By considering the Taylor series for f around 0, compute f^(90)(0).
    by the way, I don't know how super/sub script works?
    2. Relevant equations


    3. The attempt at a solution
    I tried to substitute x^5 into x's Tyler Series form and solve for f^(90)(0), but it gave me a wrong answer.
     
  2. jcsd
  3. Jan 11, 2015 #2

    Mark44

    Staff: Mentor

    Show us what you got when you did the substitution. That's the right approach.

    BTW, it's Taylor series, not Tyler series.
     
  4. Jan 12, 2015 #3
    cosx=∑(-1)^n/(2n)!*x^2n
    I am not sure what the an part: (-1)^n/(2n)! will becomes when I substitute x5 into the series.
     
  5. Jan 12, 2015 #4

    Mark44

    Staff: Mentor

    Nothing changes in that part. In your formula above, replace x by x5. That will be your Taylor series for cos(x5).

    It might be helpful to write the new series in expanded form rather than in closed form (as a summation).
     
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