# How do you find #f^6(0)# where #f(x)=arctanx/x#?

##### 1 Answer

#### Explanation:

We start by constructing the MacLaurin series for

Consider the function:

This is the sum of a geometric series of ratio:

with radius of convergence

Within the interval

and dividing by

Now consider the standard expression of the MacLaurin series of

The two series are equal only if the coefficients of the same degree in

and: