Prove that the following functions are strictly increasing: `f(x)=cot^(-1)x+x`

Prove that the following functions are strictly increasing: f(x)=log(1+x)-(2x)/(2+x) for x > -1

Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

Show that the function f(x) = 2x+1 is strictly increasing on R.

Let I be any interval disjoint from (1, 1) . Prove that the function f given by f(x)=x+1/x is strictly increasing on 1.

Prove that the function f given by f(x)=logcosx is strictly increasing on (-pi//2,\ 0) and strictly decreasing on (0,\ pi//2) .

Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

Show that the function f(x)=2x+3 is strictly increasing function on Rdot

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).