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  4. The interval in which y= ln ( ln (x)), x>1 is decreasing is

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Q. The interval in which $y=\ln (\ln (x)), x>1$ is decreasing is

AP EAMCETAP EAMCET 2020

Solution:

Given function $y=l(\ln (x)), x>1$
$\therefore \frac{d y}{d x}=\frac{1}{x \ln x}, x>1$
$\because y$ is a decreasing, then
$\because x>1 \Rightarrow \ln x<0$
$\Rightarrow x<1$, which is not possible as $x>1$
$\therefore x \in \varphi$, for decreasing