How do you find the derivative of $ln(ln(3x))$ ?

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Answer 1 · 2017-04-10T02:40:23

$[ln(ln(3x))]'=1/(x ln(3x))$

By applying Log Rule and Chain Rule repeatedly,

$[ln(ln(3x))]'=1/ln(3x)cdot[ln(3x)]'$

$=1/(ln(3x))cdot1/(3x)cdot(3x)'$

$=1/(ln(3x))cdot1/(cancel(3)x)cdot cancel(3)$

$=1/(xln(3x))$

How do you find the derivative of ln(ln(3x))ln(ln(3x))?