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Thread: Proving the exponential derivative

  1. Apr 27th, 2001, 02:50 PM #1
    Yonatan
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    Proving the exponential derivative

    How do you prove this:
    Code:
    (a^x)' = a^x * ln(a)
    I've been banging my head about it, help
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  2. Apr 27th, 2001, 03:49 PM #2
    Guv
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    Perhaps this way.

    y = a^x

    ln(y) = x*ln(a)

    d[ ln(y) ]/dx = ln(a)

    (1/y)*dy/dx = ln(a)

    dy/dx = ln(a)*y

    dy/dx = ln(a)*a^x
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  3. Apr 27th, 2001, 04:06 PM #3
    Yonatan
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    WOO!
    Thanks a lot, why didn't I think of taking the natural logarithm of both sides
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