Question

\( \frac{1}{2} \) if \( f(x)=\log _{4} \log _{4}(x) \) then \( f^{\prime}(x) \) is.

Answer 1

f ( x ) = log₄ {log₄( x )}  then f ′( x ) 

f ( x ) = [log {log₄( x )}] /log4

(log4) [ f ( x ) ] = log { logx/log4} = [ log{logx}] /  [log{log4}]

 [log{log4}] (log4) [ f ( x ) ] = log{logx}  ... differentiating w.r.to x

 [log{log4}] (log4) [ f ' ( x ) ] = 1/{logx} {1/x}

f ' ( x ) = 1/ [ (log{log4}) {log4} {x (logx) }  ]