Show that `f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x)` is increasing on `R` .

Explanation

Given,`f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x)`


On differentiating with respect to x, we get
f′(x)=`2−[(1+sqrt(1+x^2)
​​)]/(1+x^2)`

thus ,`2−[(1+sqrt(1+x^2)
)​​]/(1+x^2)`>0

Hence, f(x) is increasing in R.