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Differentiating to the power of x.

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    • Thread Starter

    Hello, I just dont know how to differentiate something to the power of x..

    For example

    y = 10^x


    Well, 10^x = e^(x ln 10) = (e^x)^ln 10, and you know how to differentiate that.

    Take logs

    y = 10^{x}

    ln(y) = \ln(10^{x})

    ln(y) = x \ln(10)

    Then differentiate (using the product rule for the x ln10)

    \frac{1}{y}\frac{dy}{dx} = \ln(10)

    \frac{dy}{dx} = y \ln(10)

    Then replace y back in

    \frac{dy}{dx} = 10^{x} \ln(10)

    what he said ^

     \frac{d}{dx} A^x -> (A^x)(lnA)
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