The formula for a Maclaurin series expansion is

The derivatives of the function e^x and their values at x = 0 are given by

            f(x) = e^x                                  f(0) = 1

            f '(x) = e^x                                f '(0) = 1

            f ''(x) = e^x                                f ''(0) = 1 

            f '''(x) = e^x                               f '''(0) = 1

            .....................                           ...............

            f ⁿ(x) = e^x                               fⁿ(0) = 1

            .....................                           ...............

Substituting the values of f(0), f '(0), f ''(0), ... into 1) we have