00:01
So this problem, we've been given a function, f of x equals 3 to the 2x.
00:06
And we need to find the derivative.
00:08
Well, what derivative rule can we use when we have this kind of an exponential equation? well, let's take kind of a generic function, a to the u.
00:19
A is going to be a constant, and u is some function of x.
00:24
When we go to find the derivative, what we're going to do is we're going to start by copying a to the u.
00:31
That's going to stay here.
00:33
Well, we need to do something with that a, that constant that we have as a base.
00:37
So we're going to multiply this by the natural log of a, whatever that number is.
00:43
Then if u is a function, we will also need to take the derivative of you with respect to x.
00:53
That's kind of our chain rule.
00:54
We have to deal, if that's a function of itself, we'll have to take the derivative of that as well, multiply it all together.
01:01
Well, let's take a look...