If `f(x)=(log)_e((log)_e x)` , then write the value of `f^(prime)(e)` .

Explanation

We have,`f(x)=log _{e}(log _{e} x)`

Differentiating with respect to X,


`f^{prime}(x)=frac{1}{log _{e} x} frac{d}{d x}(log _{e} x)`

`Rightarrow f^{prime}(x)=frac{1}{log _{e} x}(frac{1}{x})`

`Rightarrow f^{prime}(e)=frac{1}{log _{e} e}(frac{1}{e})[ because x=e]`

`Rightarrow f^{prime}(e)=frac{1}{e}[ because log _{e} e=1]`