Find the intervals in which `f(x)=x/(logx)` is increasing or decreasing

Explanation

Let` f(x)=x/logx`

​ ∴ Domain of f is (0,∞)−{1}

Now` f′(x)=(logx−1​)/(logx)^2`


For f to be increasing f′(x)>0

⇒`logx−1>0⇒x>e`

and for f to be decreasing, f′(x)<0

⇒`logx−1<0⇒x < e `

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