00:01
To compare the growth rates of these two, we're going to take a look at, well, how the growth of the inside grows.
00:07
Well, we know that lnx grows slower than x, so we suspect that ln of ln of x is going to grow slower than lnx.
00:15
So we're going to try to take the limit as x goes to infinity of, and then we'll put ln, lnx at the top, because that one's the one that grows slower, and the one that grows faster, or that we expect grows faster, we'll put on the bottom.
00:32
Now, let's apply lopatol's rule here.
00:35
So to apply lopatol's rule, we're going to take the derivative of the top.
00:38
So the derivative of the top, okay, let me put it like this.
00:43
The derivative of the top is going to be 1 over lnx and then times the derivative of the bottom, which or sorry, and then times the derivative of this, which is equal to 1 over x...