Find 9th Derivative of f(x) = cos(6x^4)-1 at x=0 | Maclaurin Series Homework

[demersal]

Homework Statement

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

 

[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.

 

[demersal]

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