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Thread: Derivative

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    Derivative

    help me find the nth derivative of x raised to the power of x ,.....i.e x^(x)
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    Re: Derivative

    Quote Originally Posted by Noahlymatic View Post
    help me find the nth derivative of x raised to the power of x ,.....i.e x^(x)
    Use the logarithmic derivative:
    $\displaystyle y = x^x$

    $\displaystyle ln(y) = ln \left ( x^x \right )$

    Now take the derivative:
    $\displaystyle \dfrac{1}{y} \cdot \dfrac{dy}{dx} = ln(x) + x \cdot \dfrac{1}{x}$

    $\displaystyle \dfrac{1}{y} \cdot \dfrac{dy}{dx} = ln(x) + 1$

    $\displaystyle \dfrac{dy}{dx} = y ( ln(x) + 1) = ( ln(x) + 1) x^x$

    -Dan
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