# 15th derivative of a binomial/maclaurin series

1. Apr 26, 2010

### karadda

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

-binomial series

3. 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?

2. Apr 26, 2010

### 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

3. Apr 26, 2010

### lanedance

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

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

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