Prove that `f(x)=x^3` in an increasing function

Prove that f(x) = x - sin x is an increasing function.

Prove that f(x)=x-sinx is an increasing function.

Prove that f(x)=x-sinx is an increasing function.

Prove that f(x)=x-sinx is an increasing function.

Prove that f(x)=x-sin x is an increasing function.

Prove that f(x)=x^(7)+3x^(5)+15 is increasing function.

Prove that f(x)=x^(2)-4x,xge4 is increasing function.

Prove that f (x) = e^(3x) is strictly increasing function on R.

Prove that f (x) = e^(3x) is strictly increasing function on R.

Let f be a function defined on [a, b] such that f'(x)>0 for all x in (a,b) . Then prove that f is an increasing function on (a, b) .