# Maclaurin Series

1. Dec 9, 2008

### demersal

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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

2. Dec 9, 2008

### Dick

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. Dec 9, 2008

### demersal

Yes, thank you very much. I think I can work it out now!