Prove that the function `f(x)=(log)_e x` is increasing on `(0,\ oo)` .

Explanation

Given`f(x)=logx`

we need to prove f(x) is increasing on x∈(0,∞)

i.e., we need to show f′(x)>0 for x∈(0,∞)

Now,

`f(x)=logx`

`f′(x)=1/x`​... [we differentiate w.r.t x]

when `x>0`

⇒`1/x​>0
...