The function `f(x)=cos^-1 x+x` increases in the interval

The function f(x)= tan^(-1)x +x increases in the interval

Function f(x)=x+ cot ^(-1) x increasing in the interval

The function f(x)=x^(1//x) is increasing in the interval

The function f(x) = (x)/(log x) increases on the interval

The function f(x) = x^2 is increasing in the interval

Consider the following statements I.The function f(x)=x^(2)+2cos x is increasing in the interval (0,pi). II.The function f(x)=ln(sqrt(1+x^(2))-x) is decreasing in the interval (-oo,oo). Which of the above statement(s) is/are correct?

The function f(x)=x/(xlogx) increase on the interval

the function f(x)=(log x)/(x) is increasing in the interval