# Maclaurin Series of Arctanx

In this tutorial we shall derive the series expansion of the trigonometric function ${\tan ^{ - 1}}x$ by using Maclaurin’s series expansion function.

Consider the function of the form

Using $x = 0$, the given equation function becomes

Now taking the derivatives of the given function and using $x = 0$, we have

Now using Maclaurin’s series expansion function, we have

Putting the values in the above series, we have