Question: The exponential function can be represented by the following power series where the ellipsis ( ) indicates that additional terms follow. The

The exponential function can be represented by the following power series

1 X. 3! 1 ebx = 1+ bx +b +b

where the ellipsis ( · · · ) indicates that additional terms follow. The notation n! stands for n factorial, such that n! = n(n −1)(n −2) · · · (3)(2)(1) for any positive integral value of n and 0! = 1. Derive the expression for the derivative of e^bx from this series.

1 X. 3! 1 ebx = 1+ bx +b +b"x" n! 2!

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