If y=log_3 (log_3x), then dy/dx=

The correct answer is Option (4) → $\frac{1}{xlogx\, log 3}$

$y=\log_3(\log_5x)$

$=\frac{ln(\log_3x)}{ln\,3}$

$⇒\frac{dy}{dx}=\frac{1}{ln\,3}\frac{d}{dx}[ln(\log_3x)]$

$=\frac{1}{ln\,3\log_3x.x}$