# Maclaurin Series for Hyperbolic Cosine

In this tutorial we shall derive the series expansion of the hyperbolic cosine function 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