If `x gt -1`, show that : `(x)/(sqrt(1+x))-log(1+x)+9` is an increasing function of x.

Show that f(x)=(x)/(sqrt(1+x))- ln (1+x) is an increasing function for x gt -1 .

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

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

Show that log(x+sqrt(1+x^(2))) 1

Statement-1: 0 lt x lt y rArr "log"_(a) x gt "log"_(a) y, where a gt 1 Statement-2: "When" a gt 1, "log"_(a) x is an increasing function.

Show that y=log(1+x)-(2x)/(2+x),x>-1 is an increasing function of x throughout its domain.

Show that y=log(1+x)-(2x)/(2+x),x>1 is an increasing function of x throughout its domain.

The function f(x)=log (1+x)-(2+x) is increasing in

Prove that (x)/((1 + x)) lt log (1 + x) lt x " for " x gt 0

f(x)=2x-tan^(-1)x-log(x+sqrt(1+x^(2)))(x>0) is increasing in