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Math Help - Need help differentiating f(x) = a^x

  1. #1
    TWN
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    Need help differentiating f(x) = a^x

    How do I differentiate f(x) = a^x

    The answer xa^(x-1) is not sufficient.

    I think I'm supposed to substitute with e somehow to figure it out, but I'm not entirely sure how e works.

    Can someone help me out? Please explain with detail.
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  2. #2
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    Re: Need help differentiating f(x) = a^x

    Quote Originally Posted by TWN View Post
    How do I differentiate f(x) = a^x

    The answer xa^(x-1) is not sufficient. CORRECT
    Note that a>0 must be the case.

    The answer is f'(x)=a^x\ln(a). It is done with logarithmic differentiation.
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  3. #3
    TWN
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    Re: Need help differentiating f(x) = a^x

    Can you explain in detail the process you underwent to reach that answer please?
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    Re: Need help differentiating f(x) = a^x

    y = a^x

    \ln{y} = \ln{a^x}

    \ln{y} = x \ln{a}

    \frac{d}{dx} \left[\ln{y} = x \ln{a} \right]

    \frac{y'}{y} = \ln{a}

    y' = y \cdot \ln{a}

    y' = a^x \cdot \ln{a}
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