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calculus

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Use logarithmic differentiation to find dy/dx for y=(1+x)^(1/x).

  • calculus - ,

    ln y = ln (1+x)^(1/x)
    = (1/x) ln (1+x)
    (dy/dx) /y = (-1/x^2)(ln(1+x) + (1/x)(1/(1+x)

    dy/dx = y [(-1/x^2) ( ln(1+x) + x/(1+x) ]
    or (-1/x^2)( ln(1+x) + x/(1+x) ) (1+x)^(1/x)

    pretty messy looking ...

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