00:01
The fact that we are given a product is telling me that we're probably asked to use the product rule.
00:10
I do want to point out that there's a lot of correct ways of doing this problem, so you don't have to do the problem the way i'm going to.
00:16
But i'm going to use the product rule.
00:20
So when you go to take this derivative, and i point out where the product is, you start by taking the derivative of the left side, which is just 2x, and you leave the right side alone, e to the 4x.
00:34
And then plus, now i'm going to leave the left side alone, and then do the derivative of the right side.
00:40
Now, the right side is really the meat of this lesson where the derivative of an exponential function is itself, and then multiplied by the derivative of the exponent, well, the derivative of 4x is just 4.
00:53
Now, some teachers are happy with this answer.
00:57
Other teachers, however, might want to see you factor out the, looks like you could factor out the e to the 4x, but you could also factor out a two in each piece...