Consider the function ƒ(x) = eˣ
(a) differentiate the taylor series about 0 of ƒ(x)
(b) identify the function represented by the differentiated series.
(c) give the interval of convergence of the power series for the derivative.

a) The Taylor series expansion of about is

Differentiating the expansion with respect to 'x' we get

b)

As we can identify from the expansion calculated above we have

c)

The interval of convergence of the given power series is

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step-by-step explanation:

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the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)