The function is .

Maclaurin series is .

Find consecutive derivatives of the function to know the pattern of the n th derivative of the function.

Differentiate with respect to  on each side.

.

.

.

.

Similarly, we can write .

Find the values of the above functions at 0.

.

Substitute above values in the Maclaurin series formula.

Maclaurin series of the function  is 

Find the radius of convergence using ratio test.

The series is  .

Consider  and 

By the ratio test the series is convergent when .

Hence the radius of convergence is .

Maclaurin series of the function  is .

Radius of convergence is .