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  • Differentiate the following w.r.t. x: log log x

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

 

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best_answer

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

Posted by

Gautam harsolia

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