How do you find the derivative of $(ln (ln (ln (x)))$ $(ln(ln(ln(x)))$ ?

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Answer 1 · 2016-09-01T14:55:27

$= \frac{1}{(ln (ln (x)))}$ $=1/((ln(ln(x))))$ X $\frac{1}{ln (x)}$ $1/ln(x)$ X $\frac{1}{x}$ $1/x$ , $x > e$ $x> e$ .

Apply function of function rule.

$(ln(ln(ln(x))))'$

$=i/(ln(ln(x))$ $(ln(ln(x))'$

$=1/((ln(ln(x))(ln(ln(x))$ $(ln(x))'$

$=1/((ln(ln(x))$ $1/ln(x)$ $1/x$

ln x is differentiable for x > 0.

ln(ln(x) is differentiable, for ln(x) > 0, and so, for $x > 1$ .

ln(ln(ln(x))) is differentiable for

ln(ln(x)) > 0, meaning ln(x) > 1, and so, x > e..

How do you find the derivative of (ln(ln(ln(x))) (ln(ln(ln(x))) (ln(ln(ln(x))) ?