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

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

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=x^(2)+2x-5

Prove that the function f(x) = 10^(x) is strictly increasing on R

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=(x-1)(x-2)^(2) .

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

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=(4x^(2)+1)/(x).

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=6-9x-2x^(2)

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=(x+1)^(3)(x-3)^(3).

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=-3log(1+x)+4log(2+x)-(4)/(2+x)

Determine the intervals in which the following functions are strictly increasing or strictly decreasing : f(x)=x^(8)+6x^(2) .