# Thread: Maclaurin series and 50th derivative

1. ## Maclaurin series and 50th derivative

The question I'm stuck on reads: Find the Maclaurin series for f(x)=sin(4x)+(6/(1-4x2)) and use that to find f(50) (0).

I know I can write both terms as separate power series from n=0 to infinity, but I'm stuck on how to find the 50th derivative given that. Thank you!

2. ## Re: Maclaurin series and 50th derivative

$f(x) = \sum \limits_{k=0}^\infty ~f^{(k)}(0)\dfrac{x^k}{k!} = \sum \limits_{k=0}^\infty~c_k x^k$

$c_k =\dfrac{ f^{(k)}(0)}{k!}$

so

$f^{(50)}(0) = 50! \cdot c_{50}$