The function is .

Maclaurin series is .

Find consecutive derivatives of the function.

Apply derivative on each side with respect to .

Since .

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Similarly, and .

Find the values of the function at .

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The maclaurin series .

Substitute the corresponding 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

If then .

By the ratio test the series is convergent .

Hence the radius of convergence is .

Maclaurin series of the function is .

Radius of convergence is .