First method:

Step 1:

The function

Find the successive differentiation of .

Step 2:

Definition of Maclaurin series :

If a function has derivatives of all orders at then the series

is called Maclaurin series for .

Substitute the above values in Maclaurin series.

.

Solution:

Second method:

Step 1:

The function

Power series for elementary function .

Replace with .

Solution:

Maclaurin series of .