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Math Help - Derivative of a^x.

  1. #1
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    Derivative of a^x.

    I am studying the attached image:
    Derivative of a^x.-capture.png

    I find myself wondering is it:
    m(a)=\lim \Delta x\rightarrow 0\frac{a^\Delta^x-1}{\Delta x}

    or is it:

    m(a)=a^x\lim \Delta x\rightarrow 0\frac{a^\Delta^x-1}{\Delta x}

    Thanks in advance...
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  2. #2
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    Re: Derivative of a^x.

    It is the first one.
    Thanks from sepoto
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  3. #3
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    Re: Derivative of a^x.

    Why then is it said:

    m(a)=\frac{d}{dx}a^x ...at... x=0

    it is confusing me if m(a) is the first one I posted. Clearly before they said:

    m(a)=\frac{d}{dx}a^x=m(a)a^x

    Thanks in advance...
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  4. #4
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    Re: Derivative of a^x.

    OK. That would mean a^x is one at x = 0. I think I get it now.
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  5. #5
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    Re: Derivative of a^x.

    Exactly.
    Thanks from sepoto
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