The question is attached. I know the power series representation of cos(x) and therefore can get cos(6x^2)/x^2 but I don't know what to do about the -1.

Any help would be greatly appreciated!

Thanks in advance!

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- May 17th 2010, 11:22 AMs3aCompute the 10th derivative of ...
The question is attached. I know the power series representation of cos(x) and therefore can get cos(6x^2)/x^2 but I don't know what to do about the -1.

Any help would be greatly appreciated!

Thanks in advance! - May 17th 2010, 12:23 PMRandom Variable
Start with the known Maclaurin series of

then

and

finally

For a Macluarin series, the coefficent of the term is

The coefficient of the term in the above Macluarin series is

so

EDIT: and (Surprised) - May 17th 2010, 12:48 PMs3a
How do you get from the before-last step to the last one? (From the one that says "so" to the one with the emoticon)

- May 17th 2010, 12:53 PMlilaziz1
the 10! came from the exponent on . If you were to take the derivative of that 10 times, you would get

- May 17th 2010, 01:00 PMRandom Variable
- May 17th 2010, 01:04 PMs3a
Oh that 10! was also tricky but I get it now! Thanks!