Why is the derivative of the exponential function itself?

The exponential function is defined as a power series, which we may (for reasons that are beyond the scope of A-level) differentiate term by term to get another power series. The general term of the series differentiates to the term before it, the first term is 1 so disappears and the series is infinite which means the whole series differentiates to itself!

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Answered by George B. Maths tutor

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