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Math Help - Exponential functions: a function of themselves

  1. #1
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    Exponential functions: a function of themselves

    Hey,

    I've read on James Stewart's Calculus (7th edition, I believe) that exponential functions are a function of themselves.

    Just like: Y= f(Y)

    how this can be? I mean, if we write things like that, we are supposing that Y is a function of Y at the current period, which is not true, exponential functions are a function of their past periods, in other words, Y at (t+1) is a function of Y at (t)
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  2. #2
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    Re: Exponential functions: a function of themselves

    I don't get what you're saying...the derivative of the exponential function is in terms of the original function, that is


    \frac{d}{dx} a^x = a^x \ln a. In particular, when a = e,

    \frac{d}{dx} e^x = e^x
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