a) You need to remember that the function decreases if `f'(x)lt0` and the function increases if `f'(x)gt0` , hence you need to evaluate `f'(x)` and to solve the inequalities above such that:

`f'(x) = (1/(1-lnx))*(1-ln x)'`

`f'(x) = -1/(x(1-lnx))`

** Notice that for any value of `x in (0,oo), ` the...**

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a) You need to remember that the function decreases if `f'(x)lt0` and the function increases if `f'(x)gt0` , hence you need to evaluate `f'(x)` and to solve the inequalities above such that:

`f'(x) = (1/(1-lnx))*(1-ln x)'`

`f'(x) = -1/(x(1-lnx))`

**Notice that for any value of `x in (0,oo), ` the values of derivative are negative, hence, the function decreases over `(0,oo).` **