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Math Help - Write a rule for f(x) = a^x where a is a constant

  1. #1
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    Write a rule for f(x) = a^x where a is a constant

    Hi
    I need to write a rule for the derivative of f(x) = a^x where a is a constant. I was thinking of xa^x-1 but my teacher said that is not what he is looking for. By the way i cant seem to get it to put the entire exponent up which is (x-1).
    Any ideas?
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  2. #2
    Senior Member topher0805's Avatar
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    The derivative of a^x will always be a^x\cdot ln a

    The way to get the entire exponent is to put it in curly brackets: {x-1}
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  3. #3
    o_O
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    Seems like your teacher is asking you to prove it?

    Note that: a^{x} = e^{ln\left(a^{x}\right)} = e^{xlna}

    If you know that \frac{d}{dx}e^{x} = e^{x} and know how to use the chain rule, then you should be able to find the derivative of a^{x}
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