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Math Help - derivative of the inverse of a function

  1. #1
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    derivative of the inverse of a function

    the function is y=x+(1/x) at y=17/4

    attempt:
    y^-1: x=y+(1/y)

    differentiate: 1=y'+ln(y)y'
    1=y'(1+ln(y))
    y'=1/(1+ln(y))

    put that over 1: 1+ln(y)

    plug in y: 1+ln(17/4)
    =approximately 2.447
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  2. #2
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    Re: derivative of the inverse of a function

    \text{If}~ y(x)=x+\frac{1}{x} ~\text{then}~x(y)=\frac{1}{2} \cdot (y \pm \sqrt {y^2-4})
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