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Math Help - derivative problem

  1. #1
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    derivative problem

    Find the derivative of

    (1+x) ^ 1/x

    can anyone help me
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  2. #2
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    Quote Originally Posted by bwong890 View Post
    Find the derivative of

    (1+x) ^ 1/x

    can anyone help me

    (1+x)^{1/x}=e^{\frac{1}{x}\ln(1+x)} , and now apply the chain rule here...

    Tonio
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  3. #3
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    i dont understand how you got that.

    can you write it out in steps please
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  4. #4
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    Quote Originally Posted by bwong890 View Post
    Find the derivative of

    (1+x) ^ 1/x

    can anyone help me
    logarithmic differentiation ...

    y = (1+x)^{\frac{1}{x}}

    \ln{y} = \frac{1}{x} \ln(1+x)

    \frac{y'}{y} = \frac{1}{x} \cdot \frac{1}{1+x} - \ln(1+x) \cdot \frac{1}{x^2}

    \frac{y'}{y} = \frac{1}{x}\left(\frac{1}{1+x} - \frac{\ln(1+x)}{x}\right)

    y' =  \frac{(1+x)^{\frac{1}{x}}}{x}\left(\frac{1}{1+x} - \frac{\ln(1+x)}{x}\right)
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  5. #5
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    Quote Originally Posted by bwong890 View Post
    i dont understand how you got that.

    can you write it out in steps please

    For all a>0\,,\,\,a^x=e^{x\ln a} . This follows at once from the very definition of logarithm
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