What is the derivative of $Ln(ln(ln(2x)))$ ?

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Answer 1 · 2016-09-05T02:00:06

$1/(( ln (ln (2x)))(ln (2x)(x))$ , $x>e/2$

For real logarithms:

ln (2x) is real, for x> 0#

ln ( ln (2x)) is real, for ln (2x) > 0, So, ln (2x) > 0. And so, x > 1/2.

ln (ln (ln (2x))) is real, for ln(ln(2x))> 0. So,

ln (ln (2x)) >0 $to$ ln (2x) > 1 $to$ 2x > e $to$ x > e/2.

All are real, for x > e/2.

In succession, apply function rule.

$(ln(ln(ln(2x))))'$

$=1/(ln(ln(2x)))(ln(ln(2x))'$

$=1/((ln(ln(2x)))(ln(ln(2x))$ $(ln(2x))'$

$=1/((ln(ln(2x)))(ln(ln(2x)))$ $1/(2x)(2x)'$

$=1/((ln(ln(2x)))(ln(2x)(x))$ , $x>e/2$
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What is the derivative of Ln(ln(ln(2x)))Ln(ln(ln(2x)))?