00:01
This question has a lot of parts.
00:01
Suppose u and v are functions of x that are differentiable at x equals 2, and it gives us all of these values.
00:06
It says, find the values of the following derivatives at x equals 2.
00:09
And there's four parts, so let's go through all of them.
00:11
So a wants us to take the derivative of uv.
00:18
Using the product rule, we can write that as u times the derivative of v, plus v times the derivative of u, and that equals u at 2, which is 3.
00:30
Times the derivative of v at 2, which is 2.
00:34
And then we have plus v at 2, which is 1 times negative 4, which is the derivative of u at 2.
00:42
So we get 6 minus 4.
00:47
The second part, we have the derivative of u over v.
00:58
And to do this, we use the quotient rules.
01:01
So we square what's on the bottom, bring it back on top, and differentiate the numerator, then subtract out u the root of v, because you differentiate in the other order now...