What is the derivative of ln(ln(x))???

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  • Anonymous
    1 decade ago
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    your u will be the ln(x)

    your du will be 1/x dx

    Then you just plug and chug and it all comes out to equal

    1/(xln(x))

  • 1 decade ago

    think of this as the chain rule. Let's take the derivative of ln(u): it's u'/u, right?

    If we used substitution and pretended that u=lnx, the original problem would look like ln(u).

    we know the derivative of u. since u=lnx, u'=1/x.

    ok so the derivative of ln(u)= u'/u = (1/x)/lnx = 1/(xlnx)

    keep in mind that all values of x are the absolute value of x so it's really:

    1/|x|ln|x|

  • 1 decade ago

    by chain rule >> (1 / ln x) (1 / x) = 1/ (x lnx)

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