Prove that the function are increasing for the given intervals: `f(x)=e^x+sinx ,x in R^+`

Prove that the function are increasing for the given intervals: f(x)=sin x+tan x-2x,x in(0,(pi)/(2))

Prove that the function are increasing for the given intervals: f(x)=sec x-csc x,x in(0,(pi)/(2))

Prove that the following functions are increasing for the given intervals, (i) y =e^(x) + sinx, x epsilon R^(+) (ii) y=sin x+ tan x- 2x, x epsilon(0, pi/2) (iii) y = x + sin x , x epsilon R .

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

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

Prove that the function f(x)=log_(e)x is increasing on (0,oo)

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

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

The function f(x)=x^(2)+2x-5 is increasing in the interval