Question

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

Answer 1

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

Explanation:

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))`