# Math Help - Maclaurin Series

1. ## Maclaurin Series

Hello, I have a problem that says: Compute the 6th derivative of:
at x=0.
So I know that $f(x)=\sum_{n=0}^{\infty}(-1)^n\dfrac{\left(\frac{x^2}{4}\right)^{2n+1}}{2n+1 }$
But I'm not sure how to go about and solve it.
Thanks,
Matt

2. Originally Posted by matt3D
Hello, I have a problem that says: Compute the 6th derivative of:
at x=0.
So I know that $f(x)=\sum_{n=0}^{\infty}(-1)^n\dfrac{\left(\frac{x^2}{4}\right)^{2n+1}}{2n+1 }$
But I'm not sure how to go about and solve it.
Thanks,
Matt
Use the fact that the general form of a Maclaurin series is $\sum_{n=0}^{\infty}\frac{f^{(n)}(0)x^n}{n!}$ and compare coefficients to find an equation for the n-th derivative

3. Hmm, I'm still having some trouble with this problem, could you show me what to do exactly? I know that the maclaurin series is x-x^3/3+x^5/5-...
So would I compare -(((x^2/4)^3)/2) to ?