# Q8  Differentiate the following w.r.t. x:   $\log ( \log x ) , x > 1$

Given function is
$f(x)=\log ( \log x )$
Lets take $g(x ) = \log x$
Now, our function reduces to
$f(x) = \log(g(x))$
Now,
$f^{'}(x) = g^{'}(x).\frac{1}{g(x)}$                   -(i)
And
$g(x)=\log x\\\Rightarrow g^{'}(x) = \frac{1}{x}$
Put this value in our equation (i)
$f^{'}(x) =\frac{1}{x}.\frac{1}{\log x} = \frac{1}{x\log x}$
Therefore, the answer is $\frac{1}{x\log x}, \ \ x>1$

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