Use any approach to find the Maclaurin series

[MarkSA]

Hello,

Use any approach to find the Maclaurin series for:
f(x) = x^3 * cos(x^7)

What would be the easiest approach to do this problem?

I'm thinking I can derive a series for cosx easily, and then substitute x^7 in and multiply the entire resultant series by x^3 to end up with a Maclaurin series for the original f(x). Does this sound reasonable? Or is there an easier way to do this one? I can't think of anything else. If I take the derivatives of the entire function it gets really messy really quick.

 

[pka]

Yes it is reasonable and this will help,
\(\displaystyle \cos (x) = \sum\limits_{k = 0}^\infty {\left( { - 1} \right)^k \frac{{x^{2k} }}{{\left( {2k} \right)!}}}\)