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The formula for a Maclaurin series expansion is


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

 

            f(x) = ex                                  f(0) = 1

            f '(x) = ex                                f '(0) = 1

            f ''(x) = ex                                f ''(0) = 1 

            f '''(x) = ex                               f '''(0) = 1

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

            f n(x) = ex                               fn(0) = 1

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



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



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