Maclaurin Series

  • Thread starter demersal
  • Start date
  • #1
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Homework Statement




(1 pt) Compute the 9th derivative of:
f(x) = [tex]\frac{cos(6x^4)-1}{x^7}[/tex]
at x=0.



Homework Equations



Hint: Use the MacLaurin series for f(x).

The Attempt at a Solution



I have tried many weird ways and cannot come up with the correct numerical answer. I've gotten 0 each time and it still comes up as wrong. Please help point me in the correct direction, even if it is only a verbal explanation!

Thanks so much
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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The only term in the expansion that would contribute to a 9th derivative would be the term containing x^9. If you look up the Maclaurin series of cos you'll it can be written as a sum of even powers of it's argument. The fourth power of 6x^4 contains an x^16. 16-7=9. Is that enough of a hint.
 
  • #3
41
0
Yes, thank you very much. I think I can work it out now!
 

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