okay so i took the first 7 derivatives and evaluated them at zero and got:

1,0,-9,0,81,0,-729,0,...

so, if you remove the zero terms, you know that the series is alternating.. and it looks like there's a (-9)^n term in there

what i'm confused about is how to find the nth derivative at zero, and how to just isolate the nonzero terms of the series..and then i'm not sure how to plug it in and continue from there