15th derivative of a binomial/maclaurin series

[karadda]

Homework Statement

sqrt(1+x^4)

use the binomial series to find the maclaurin series for the above function. then use that to find the 15th derivative at 0.

Homework Equations

-binomial series

The Attempt at a Solution

I've gotten to:

$$\Sigma$$ (k n) (x^(4n))
from n=0 to infinity

How can i use this to find derivatives?

 

[lanedance]

i haven't checked what you've got to...

but if you write out the form for a maclaurin series in terms of its dereivatives, fror ecach term, notice the power of x & the order derivative in the coefficient are always the same

 

[lanedance]

$$f(x) = f(0) + \frac{f'(0)}{1!}x+\frac{f^''(0)}{2!}x^2+..+\frac{f^{n}(0)}{n!}x^n+..$$

$$f(x) = f(0) + \frac{f^{1}(0)}{1!}x^1+\frac{f^{2}(0)}{2!}x^2+..+\frac{f^{n}(0)}{n!}x^n+..$$