Given: f (x) = 2x + cot-1 x + log [√(1 + x2) – x]
To show: the given function is increasing in R.
Applying the sum rule to last part we get
Now adding by taking the LCM, we get
Now for any real value of x, the above value of f(x) is greater than or equal to zero
And we know, if f’(x)≥0, then f(x) is increasing function.
Hence the given function is increasing function in R.