Simple. If the function is increasing on an interval its first derivative will be positive. Likewise if the function is decreasing on an interval the first derivative will be negative.

For example:

The denominator of this is always positive (unless x = 0), so the numerator is the only thing that determines where the first derivative is positive or negative. So let's find where the numerator is 0:

And we immediately see that the numerator is NEVER 0 (for any real x, anyway.) So the function is either always increasing or always decreasing. So pick a convenient x value (x can't be 0 remember!), say x = 1000000 will do. It is easy to see that is positive.

Thus the first derivative is always positive, so the function is always increasing on its domain. So:

The second problem is done in a similar manner.

-Dan