Why is it that the constant e is defined as being the unique case where the limit as h goes to 0 of (e^h - 1)/h = 1? I mean every exponential function like a^x equals 1 when x equals 0, right? So would it be fair to say that (a^h) approaches 1 as h approaches zero? And that (a^h - 1) approaches zero as h approaches zero? And finally that the limit as h goes to 0 of (a^h - 1)/h also equals one?(adsbygoogle = window.adsbygoogle || []).push({});

I am confused as to why is it that only e is such that d/dx(e^x)=e^x

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# Derivatives of Exponentials (why e?)

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