00:01
Okay, so we're going to be trying to find the derivative of this function, y is equal to log base x of e.
00:08
The way that we're going to do this is we're first going to take x and raise it to both sides of this equation.
00:14
And so we have x raised the y power is equal to x raised to log base x of e.
00:20
And then whenever we have x raised a log base x of something, it's going to be equal to whatever we're looking at the log of.
00:26
So we have here x to y is equal to e.
00:29
And that makes sense since log base x of e is going to be equal to whatever number gives us a value equal to e when we raise x to that value.
00:37
So we're raising x to that value, which means we're going to get a number equal to e here.
00:42
And so we have x the y is equal to e.
00:44
The next thing we can do is take the natural log of both sides.
00:47
So we're going to have the natural log of x raise the power of y is equal to the natural log of e...